12 Monkeys addresses, among other things, the paradoxical nature of time travel (and time travel movies) in a parodoxical way. The movie is highly circular and incestuous: It is the year 2035. A deadly virus (unleashed in 1996) has destroyed most of the world's population, enabling the animals to rule the world again. The human survivors move deep underground and build their cities there; cities that seem to be mostly composed of prison guards and prison convicts.
James Cole (Bruce Willis) plays a prison convict/time traveller from this dystopian future who "volunteers" to be sent back to 1996 in order to allow his virus-ravaged world to move back to the surface. He cannot change the events of his past. All he has to do is bring back a pure sample of the virus so his people can overcome it and become the rulers of the planet.
However, time travel in the year 2035 isn't perfect yet (probably because they have "ex-insurance agents" in charge of it). The first time he is sent back, he ends up in the year 1990, where he is promptly put in an asylum. He then meets two of the people who play key roles in the destruction of the human life on this planet: his psychiatrist Kathryn Reilly (Madeline Stowe) and co-asylum inmate Jeffrey Goines (Brad Pitt).
The plot is set up so it looks as though Cole is responsible for Doomsday. His ramblings about the virus influences Goines' plans, once his father (the Nobel prize winning virologist whose lab coincidentally keeps an amply stock of the deadly virus at hand) gets him out of the asylum. Goines then goes on to become the leader of the Army of the 12 Monkeys, who the people in 2035 believe are the ones responsible for unleasing the virus.
Meanwhile, the scientists in Cole's future bring him back and have another go at putting him in the right year. This time, after a couple of bumps (notably one in WWI where Cole is shot in the leg), he ends up in the right year where he once again ends up with Reilly and manages to convince her of his story. However, Reilly's psychiatry and the continuous time travel appears to have taken its toll on Cole, and when he is brought back to 2035 and sent back to 1996 again, he is convinced that he is just a mental patient with delusions about the future. This time, however, Reilly convinces him otherwise and together they try to stop the Army of the 12 Monkeys.
History can lie. Cole discovers this (in 1996) and passes this on to the future (2035) and becomes a hero. At this point, there are numerous options to end the story after tieing up the lose ends. But the story is left very open-ended and the issue of whether there are more loops in the future and the question whether the past can really be changed is left unexplained and unanswered.
Viewers of this movie may recall a Star Trek: The Next Generation episode where the Enterprise is caught is a time loop of destruction, and each time the crew travels back through time, they experience a deja vu sensation that finally allows them to break out of the destructive loop. The memory Kathyrn Reilly experiences, that she has seen James Cole before, could be one such instance. Thus viewers who like happy endings may wish to imagine another loop where Reilly and Cole actually manage to save the world. Viewers who like complete endings may wish to imagine that the people in 2035 were eventually able to go back to the surface with Cole's help. Cynical viewers may opt for an ending where nothing changes and everything the people in 2035 do ends up being futile. Finally, for those of you who are familiar with the Everett multiverse interpretation of quantum theory, each of the contradictory events in the movie could be happening in a different universe. For example, there may be a universe where Cole survives and lives happily everafter with Reilly, one where Cole survives but is too late to stop the virus, and one where Cole is never sent back into time.
While the main focus of this review is on the plot itself, the movie is worth watching for its amazing cinematography, excellent acting by all the people involved, and the sci-fi effects.