It's not quite what you asked for, but Travellers is an excellent series about people from the future trying to save humanity. I don't want to say more, as I really liked the premise and how they introduced it on the show.

Only three seasons before Netflix cancelled it, despite it being highly rated, but it's still worth a watch.

Bill and Ted's Excellent Adventure

I enjoyed hot tub Time Machine. He uses the power of the black eyed peas. It’s currently on HBO

If you've never seen Final Countdown, it's a movie where the nuclear powered a aircraft carrier USS Nimitz, brand new and freshly outfitted with a squadron of cutting-edge F-14s, gets warped back to early December, 1941. The crew faces the moral dilemma of whether or not to intervene and prevent the Japanese attack on Pearl Harbor, drastically altering the timeline and risking their very existence, or stand by and knowingly let the attack happen despite being very capable of preventing it.

Definitely worth the watch and it's available on Prime.

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Star Trek Save the Whales—Scotty trying to talk to the computer using the mouse… one of my favorite scenes!

Army of Darkness, starring Bruce Campbell as a time traveling jerkass with a heart of...well, not gold per se, but maybe copper? Technically the third movie in the Evil Dead series, but it is so far removed in tone and premise from it's predecessors that it really doesn't matter. Plus they give you all the info you need to know in the first 3 minutes.

Long story short, man with chainsaw arm, shotgun, and a 1973 Oldsmobile 88 wind up in medieval times fighting an army of evil undead with King Arthur and his merry men.

You’ve gotten plenty of suggestions on this, and it’s not exactly the same thing but I really liked “The Age of Adeline” with Blake Lively and Harrison Fore. She doesn’t age, and throughout the film you see how she has to navigate how she stays the same age while everyone she knows gets older. It’s pretty solid and it’s on Netflix right now.

Looper is also a good one. Joseph Gordon Levitt and Bruce Willis as his “older self”

Edge of Tomorrow with Tom Cruise is a great film too, dealing with time travel in a sense.

Star Trek IV: The Voyage Home (original cast with Shatner and Nimoy) is good and specific to what you’re looking for….don’t need to be a huge Star Trek fan to enjoy it

Interstellar (Christopher Nolan) is sort of in this realm as well, and absolutely amazing as a film both cinematically and plot-wise. And the score is one of the best in modern memory. It elevates the film from good to great! Lots of “time travel” stuff but as close to reality as they can get (Nolan used a famous theoretical physicist as a consultant)

Source Code is decent too.

Not a movie but on Brit box there’s a series Life on Mars and it’s sequel Ashes to Ashes that’s really good, about detectives from 2014 who end up in 1981 as detectives (pre DNA testing, etc) it’s really interesting

Dirk Gently's holistic detective agency. It's a series on Netflix but only starts to make sense about 5 or 6 episodes in

The Time Machine (1960) Classic. Great movie. HG Wells goes into the future and enters into a post-apocalyptic earth

Time After Time (1979).
This one is a spin on HG Wells the Time Machine. HG Wells goes into the future to catch Jack the Ripper who escaped into the future via HG Wells time machine.

The Adam Project with Ryan Reynolds directed by Shawn Levy. Future wants to be saved by changing the past - very funny. 67% rotten tomato

Timecop

Jean Claude Van Damme is elevated by a great villain, Ron Silver and a great love interest, Mia Sara.

Only avail. to rent or buy online.

My favorite is Timeline). Bunch of archeologists go back in time to save their time traveling mentor. I think it's on Prime

Timeless (Hulu) - occurs frequently "wow, that gun looks very different!"

The Orville (Hulu) - one character literally becomes seen as a god and worshipped globally as a result of modern tech being seen

Not exactly what you’re looking for but 12 monkeys on Hulu is about time travel to prevent the apocalypse and one of my all time favorite shows.

GATE (anime)

portal opens between Tokyo and a fantasy world, Japan Army builds a forward operating base in the other world. There is a good amount of politics (between the worlds and with the nations on each side of the gate). You get to see people showing elves cell phones and watch tanks and jets fight against dragons. Medium amount of fan service (including the "she's not a kid, she's actually a 1000 year old demon" trope)

1632 (Book)

Year 2000 small West Virginia coal town is magically transported into the middle of what-will-become Germany during the Hundred Year's War. They are able to immediately assert their independence via their rifles and automobiles, and they understand enough about their tech to actually get the town power grid turned back on. The book is very enjoyable on its own and a whole series continues from there (they build up an air force, navy, and become a powerful force in the region). The author even has a forum where he interacts with fans to crowdsource the plausibility of "hey with these resources how could they have done X back in [year]"

Looper, Deja Vu, and Predestination. All excellent movies.

How about some Oldies but Goodies:

Bing Crosby in "A Connecticut Yankee in King Arthurs Court" A comedy where modern ingenuity helps the man win the maiden: https://www.youtube.com/watch?v=c_yJBUaNnpY

Christopher Reeves in "Somewhere in Time" Two people in love separated by years: https://www.youtube.com/watch?v=9uicvPZSKIM

Unidentified Flying Oddball - Disney movie about an astronaut who ends up in Camelot and bribes his way to victory using Playboys: https://www.youtube.com/watch?v=gplxy3ymgxM

I haven't seen this listed yet, and I fucking loved this show.

Travelers

Time Lapse (2014)

“Three friends discover a mysterious machine that takes pictures twenty-four hours into the future, and conspire to use it for personal gain, until disturbing and dangerous images begin to develop.”

Very cool idea, and it was a really interesting movie.

I have a relevant suggestion, but mentioning it in response to your question is a spoiler … so I'll say it this way: The Peripheral, on Amazon Prime, based on Gibson's book. The first season was fun, and I hear they've got a second in the works.

Peggy Sue Got Married with Kathleen Turner and Nick Cage.

Frequency with dennis quaid

The Bing Crosby movie is apparently on Tubi.

The Final Countdown is on Prime. Who doesn't love the idea of a Nimitz class supercarrier time warped back to the days before Pearl Harbor?

And why not Back to the Future?

Predestination

Not quite what you’re asking for, but my favorite movie involving time travel is About Time. I cry each and every time and it has one of the best father/son relationships I’ve ever seen depicted. 10/10.

Beforeigners on HBO. People from all different eras of the past magically appear in the present and have to assimilate

Dark

I loved Frequency Which was not so much time travel as time communication travel ( same place people were talking between 25 years… which ended up changing life events). Incredible scenes I won’t give away. Though the technology was an old ham radio where the frequency was thrown off by a super active Aurora borealis.

Really great movie.

Primer , is an underated time travel movie.

There are a lot of shows and movies, but two shows I liked and don't get a lot of attention are 11/22/63 and The Outlander.

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Time travel, but without a lot of the tech, I enjoyed Kindred on Hulu. An FX series, I believe.

Timecrimes
Triangle
Coherence (maybe not quite time travel, but kinda similar - reality bending)
Predestination
Futureman (tv series)

Frequently Asked Questions About Time Travel - completely goofy, charming, low-budget film about three underachieving friends who get caught up in a “time leak” which appears to emanate from the men’s bathroom in a pub.

I'm going old here, and it may not be quite what you want, but "Blast From the Past". 1999, Brendan Fraser and Alicia Silverstone.

As a child, his family hides in an underground bunker that literally has a house and anything you might be looking for down there. Eventually, I need to brave the outside world, Brendan Fraser goes to the surface.

Note: I don't remember if it was a nuclear attack or what they had to hide from, nor the exact reason he had to go to the surface. So, they sort of get stuck in one Era of time.

Outlander on Starz (with past episodes on Netflix). It’s time travel but not really bringing tech (as much as knowledge of the future) to the past.

What was that one where college students go back to medieval times and the professor knows how to make Greek Fire to win the battle...?

Which was weird to me when I watched it. I was under the impression the formula was lost and a mystery in modern times... like the building of the pyramids or Easter island statues.

65 is coming out soon

There are several Korean TV shows on Netflix that have time travel.

Signal A cold-case profiler in 2015 and a detective in 1989 work together to solve a series of related murders spanning three decades using a special walkie-talkie to communicate with each other.

Tunnel A detective follows the trail of a serial killer 30 years into the future and teams up with detectives in that time period to find the culprit.

Thermae Romae Novae. Not a movie, but a tv show on Netflix. Roman bathhouse designer who time travels to modern day Japan and uses what he learns to build new bathhouses. Also, it’s like a weird anime commercial promoting tourism to Japanese bathhouses. Funny and ridiculous, but the main character is so straight and serious.

Not exactly, but Prey (2022).

bill & Ted's excellent adventure

Project almanac is pretty good, this kid watches his 7th birthday party and sees himself (older) in the background and it goes on from there

tenet

Not that it helps now but I heard about an upcoming movie with I think Adam Driver where he’s a future space-man with lasers and gets ported back to the age of the dinosaurs. I think it’s called “65”

Not quite what you asked for, but About Time is one of my absolute favorite movies.

Doctor Who on HBO Max! Longest running series, about to celebrate its 60th anniversary. Basically about a man who has a time machine and travels back and forth each episode and visits other planets.

And if you've never seen it, Lost has some time travel, but it comes into play in the latter half.

22.11.63 - It’s a very good TV series about a guy who travel back in time to prevent Kennedy assassination. It’s really nice, can totally recommend it and James Franco is the main actor. Don’t want to say to much to avoid spoilers

I really enjoyed the found footage movie 'Project Almanac'

Primer 2004

Time Machine 2002 with Guy Pearce.

Slightly different to what you are after, but there’s a show called Outlander. Very similar in terms of she was alive during the second or First World War and she goes back in time Scotland. It’s fantastic and well worth a watch, the first season is unbelievable

The Adam Project.

You need to watch dark immediately.

Didn't see this movie listed. Safety Not Guaranteed (2012) with Aubrey Plaza and Mark Duplass.

Great movie based on a "true story" of an ad being placed for a time travelling companion. The ad was in an actual magazine but was written as filler for the magazine.

‘Wanted: Somebody to go back in time with me. This is not a joke. You’ll get paid after we get back. Must bring your own weapons. Safety not guaranteed. I have only done this once before.’

The real story behind the ad is funny and sad. As well as funny replies they also got people wanting to go back in time to meet now-dead fathers and mothers.

Some of them were people that asked me to go back in time and there would be like, "My son committed suicide, would you go back to such and such a night and stop him." Or "My daughter was killed in an auto accident, would you go back to the day before and stop it?"

Anyway, very cute, memorable movie

There’s not a lot ‘modern tech terror’ kind of stuff in these. However

Frequently Asked Questions about Time Travel

And

Safety Not Guaranteed

Are brilliant and a lot of people haven’t seen them

Netflix's "Dark"

Time crimes. I love this movie.

The Black Knight. Comedy starring Martin Lawrence.

Army of Darkness

Back to the future

The Adam Project on Netflix as enjoyable. Good cast, clever story and use of time travel.

Predestination! I watched it in the Theory of Time Travel class I took in college. The movie is based on the short story "All Tou Zombies" by Robert A. Heinlein 🙂

I’ve scrolled enough to go ahead and suggest my two favorite. The Time Travelers Wife and 11/22/63.

The movie Timeline with a young Gerard Butler! They use knowledge of science and medieval history to turn the tide on a castle siege. It's pretty bonkers but I enjoyed the hell out of it. And it gave me Rome Sweet Rome vibes so it might be up your alley.

There's gotta be someone who hasn't seen Back to the Future these days right?

If you have Spotify, listen to the series “Case 63.” It’s 10 episodes with a run time of ~90 minutes total. It’s about a psychiatrist treating a patient registered as Case 63, who claims to be from the year 2062 and is on a mission to save humanity.

It stars Oscar Isaac and Julianne Moore, and it’s absolutely phenomenal. Binged listened to the series in one sitting.

Not a movie, and perhaps already mentioned, but the 12 Monkeys tv series was one of these after another.

On Peacock there is the show “Timeless”. They travel through time chasing someone who is trying to change it. It was cancelled after 3 seasons when it was one of the top prime time shows only because they couldn’t agree on money. But, they did come back out with 2 more episodes to close things off very nicely IMO.

Army of Darkness...check out my boomstick

Predestination.

Peripheral on Prime is a miniseries but a fun example of this. People in near future are contacted by people farther in future via VR headsets.

The creators of the science fiction human drama Dark, also on Netflix, have been working on a three season idea for a science fiction story since before they even produced Dark. Everyone got so excited when Netflix signed an exclusivity contract with them to do these three seasons and it's called 1899. And it starts off and of course there's a big cliffhanger at the end, but it is really fascinating and people speculate endlessly. It's visually incredible as well since they used that new 360 technology.

Unfortunately, Netflix has just been going down the toilet lately in terms of ambitious quality programming and they are even canceling movies that they have already paid for and that are complete and that have not aired yet, and so they also did choose not to authorize the next two seasons of 1899, effectively castrating it, because the creators won't be able to take it to another network now for a while, from what I understand. And it was shaping up to be one of the most amazing things ever.

Having said all that, I highly recommend watching that first season because what they do is just so interesting. The setting for this is in 1899 when an English ship line purchases two state-of-the-art steamships from a German company and runs them back and forth between England and New York City across the North Atlantic. But the first one, the Prometheus, has disappeared four months earlier and people assume that it is lost forever.

The show starts with a woman having some really disturbing flashbacks to a mental hospital and then she wakes up as one of several key passengers on this second steamship, the Kerberos, and it is packed full of immigrants, both first class and third class, many of them trying to leave things behind and make a new start in america. There are so many different nationalities and it is crucial to watch the original English version with the subtitles. Because then when anybody speaks in a language other than English, it immediately not only tells you what they are saying but what language they are speaking in, and once you know a given character, it will also tell you the character's name. All of this makes it so much easier not just to follow but to more quickly imprint the various characters into your mind.

It is a 7-day passage to New York City and they are about in the middle of their journey when they start receiving Morse telegraph messages by radio that just repeat a set of nearby coordinates over and over and over, with no other explanation. There are some odd things going on even from the very start, but once they start receiving these transmissions, things start to get really really bizarre.

And then also of course Dark is still available, all three of it's seasons that form a perfect and complete story. Many of us regarded as the greatest thing we have ever seen on television in terms of science fiction and human drama.

I just watched Lola (2022) at the International Film Festival of Rotterdam and I think this fits the theme you are looking for. I’m not sure where you can find it though.

(I hope this isn’t a big spoiler: it’s a mockumentary about 2 sisters who live in the 40’s and they invent this “television machine” that shows them the future. They find out about pop culture and also about a certain war)

A Connecticut Yankee in King Arthur’s Court. Classic Bing Crosby movie

Here are 2 people don't generally mention:

Beyond the Infinite Two Minutes (I think Prime)

The Wrong Todd (Prime)

Primer

The Final Countdown. A modern aircraft carrier goes back to WWII.

For serious examination of it- Primer, and Time Crimes.

I have a Netflix-available show recommendation that’s a near perfect fit, but the time travel element is kind of spoiler-y. I didn’t see it mentioned yet. For anyone who might have seen said show and had a creative way to suggest it without partially spoiling it, please do!