In my opinion, we didn't achieve yet time travel, because we never tried to activate a time machine yet.
I think time travel could be only toward the future, unless we find out how to warp travel...

1. Time travel + Technological singularity " The all-cheats activator machine "

One of the theories is that activating time travel would be like activating the final cheat in a videogame, the one who unlocks everything. This kind of time travel would preserve some sort of free will, because we would never meet any future time version nor any past time version. We would simply unlock all of future technology in a instant. It becomes more like a " time advancer ", causing the end of history, the end of linear time, and advancing of progress in a unimaginable way.

2. Time travellers visit the present from the future " The Museum World "

In this version, there is not free will, because after the first time travel, thousands of time travellers, or maybe, some time travellers ( secret missions ? ) will enter this world and arrive from the future.
These people would be aware of the future events, and probably, anyway, history wouldn't be changeable ( possibly ) but only just observable.
The world becomes a museum in which history is revisited from future people.
They might choose to not be observable from us, or perhaps there might be interactions between time.
This version implicates one universe, one timeline, and not multiverses.

3. Time travel into the multiverse " Impossible things become possible "

This is what time travel would be if there are many other dimensions, and many other universes beyond this.
Probably other dimensions would be set in the past, remote or recent, and other ones in the future, remote or recent.
We could communicate and interact in a more free way, because there wouldn't be consequences for our own universe.
People might be able to move into other dimensions and never come back.

If there is a multiverse out there, there isn't any death. People who die will still be alive in another universe in which they survived.
We would discover the secret behind death.

4. Warp travel into the past " Beyond the nuke: this might destroy the whole thing "

This is some kind of dangerous time travel. History becomes flexible, it would mean, it can be changed, and a person would be able to re-shape a world and its history.
Mistakes would cause history timelines to delete and be replaced by total different outcomes.
Governments would send people to correct history, eventually creating a worst history ( in my opinion ).
People would become insane and time would lose its meaning.
Sudden disappearance of your life is always possible, you could find yourself in another timeline every second and chaos would reign in this planet.
People who want power would find the tool of highest temptation...Time travel would be dominated by wrong minds.
This would never be given/shown to public world, It may rest private.
Life would sure become an eternal adventure.
History itself would find a way to fight humanity correcting events, making possible for some other people to create their own timeline.
Correcting mistakes of humanity would lead to bigger consequences.

5. Time travel changes the past " The cause is in the future "
Intra-dimensional time travel " Some other universe invents time travel and we are caught in the interference "

This kind of time travel would consist in this: after the first time travel, a reverberation into the past would cause the past to change and " adapt " to the present event.
Its like throwing a rock into a pond. The environment ( in this case, the timeline ) has to adapt.
This is some kind of an interference event, that may cause even the future to change.
Its again the year zero...The present becomes more powerful than past and future.
We would see both causes from the past and from the future.
Imagine that time travel wasn't supposed to happen. But it happens because of an interference. Say, we didn't discover yet another universe, and in this other universe they invent time travel.
We didn't know yet that some events could influence both timelines.
This may happen even without a time machine...It would mean suddenly, in some yet unforeseen way, we become able to visit the future, or say, see the future, remember the future or something like that.
Imagine that there are certain events that once a singular universe makes them real, the same thing becomes a reality in all of the other ones.

We can now discuss all these theoretical ways for time travel to become real.

just marking for later

Originally posted by Zagari
5. Time travel changes the past " The cause is in the future "
Intra-dimensional time travel " Some other universe invents time travel and we are caught in the interference "

This kind of time travel would consist in this: after the first time travel, a reverberation into the past would cause the past to change and " adapt " to the present event.
Its like throwing a rock into a pond. The environment ( in this case, the timeline ) has to adapt.

I like #5. In some ways I think this is already happening naturally without technology. That is: events are making ripples not only forward but backward in time. Initially that would seem to create paradoxes but I think the universe conserves paradoxes in various ways. The possibilities hint toward the idea of many universes constantly splitting and merging. The matter/anti-matter distinction seems to me like one such paradox that the verse couldn't get rid of.

As far as only being able to travel forward, that would be relatively easy if we had black hole in our back yard. To go back in time we'll have to bend space (as you said: warping).

I think we'll be sending bits of information backward and forward soon. It might not be classical information, but a type that transcends space-time (1-dimensional information). We still have much to learn about entanglement but my outlook on possible future time-travel technologies continues to look more probable.

Before anyone talks about time travel to the past, I want you to explain to me how you are going to land at a safe spot on the earth when you get to your desired point in the past? Does your time machine also move you through space, because I can assure you that 3 days ago the earth was not in the same place.

And how accurately could anyone fix a location on earth at any significant point in the past? Could you specify the coordinates of your living room 1 month ago accurately enough so that you don't land in a wall, or the floor, or 30m up above your house? Wouldn't you need to factor in that the earth revolves on it's axis, orbits the sun, co-orbits the center of mass of the earth-moon system, orbits the milky way with the sun, and the milky way's motion in our local cluster?

Fine, you go 6 months into the past, but where will you be? How are you going to aim at a proper location for your arrival?

There are more than 5 theories - just look at the Sci-fi shelves of any library or bookshop!

Opens up a plethora of alternatives.
How many of you, during the earlier part of your life (or maybe even later) have had a "deja vu" experience? I have had many, especially in my teens when I had that uncanny feeling of having 'been here' before. On one occasion I was coming down some steps backwards when I instinctively halted for a fraction of a second as I 'knew' I would fall and break my leg if I continued. The experiences have been few and far between but imagine if these events were simply portals for us to come back from the future and re-enter our world again? Could we manage to concentrate on one of those events prior to sleep and experience that "deja vu" moment as we woke up? No space travel machine would be needed. Could we recall the future from whence we came?
In such an event surely the dimension from which we came would come with us (thereby ceasing to exist) in which case we could 'start again' and not make the same mistakes. Would we retain the knowledge from our experience in the future and make ourselves rich? Would we be better people for it?
The mind boggles.

Timetravel has been going on for sometime however it will not be done for another 137yrs CERN almost do it later this year but mess up. Thanks to them an there big bang games they tear a hole in the fabric of time not to meantion the worm hole that they will close but not with out a great cost to mankind. There are a number of Tempus Viator on this planet however you would never know. They are all here for a reson and no none of it bad. The Tempus Fugit programme was set up sorry will be set up in about 149yrs 2161. It is not of earth so those of you who think it will be in your life time sorry no can do. I know of 8 Tempus Viators that came here between 1964-1978 after that something happened and nomore have come and of those 8 only 3 remain. It is thought that the programme got damaged on the last Tempus Fugit. Oh by the way if you think this is just the ravings of a madman please check mankinds so called breakthroughs in the world of computers. In the past 15yrs you have gone massive desktop bulky labtops to tablets and handhelds that have more power than what was used to first send mankind in to space. Also how can battarys found over the past few years be explianed when the date back thousands of years???? photos have been found with people dressed out of the ordinary or objects found that should not be there.