The dystopian genre is one that any science fiction fan should be very familiar with. Technically speaking it could be applied to any genre, but it is commonly associated with science fiction if only because of the fascinating worlds that can be created when the two are combined. From the towering skyscrapers and machine-like workers of Metropolis to pollution-choked Los Angeles in Blade Runner to the crime-filled world of Escape From New York, a variety of different worlds have been created combining the science fiction and dystopian genres.
We are introduced to our hero, often in a world that is obviously corrupt in some form or another. Usually they are an ordinary individual going about doing their part in the society, but there is something that makes them stand out from other conformists. At some point, some new element is brought up that makes the protagonist an outcast from his or her world. Their eyes are suddenly opened to what is really going on and they are left to question the ethics of the world in which they lived, which in turn often leads to them being drawn into or forming a resistance (or otherwise rebelling against the government) and eventually culminates in a revolution that ends with the implication of a better future.
Now there are a ton of films that could be fit into this structure: Metropolis, Logan's Run, The Running Man, Total Recall, Dark City, The Hunger Games, Elysium, and Divergent. With some slight tweaking you could even fit in Jean-Luc Godard's Alphaville. Heck, this plot isn't even strictly confined to science fiction, as The LEGO Movie of all things follows this basic structure. Granted there are variations in the details, but usually the same structure is applicable.
Now the details may vary: the heroes may be ordinary people, rogue law enforcement, or outsiders, but whatever happens there is usually some sort of catalyst that causes them to rethink their life and compels them to rebel against the dominant authority.
In Metropolis, it is Freder's first encounter with Maria, which leads him to search for her through the lower levels of the city where he witnesses (and at one point experiences first-hand) the horrible conditions faced by the workers to keep the upper levels of the city going. In The Running Man, it is Ben Richards refusing to fire on civilians, which causes him to be arrested and then framed for the mass murder he refused to commit. Logan 5 in Logan's Run stars off performing his job to catch runners by posing as one only to find himself in that position for real. The Hunger Games has Katniss being forced to volunteer to prevent her sister from being forcibly taken in a battle to the death. Beatrice in Divergent has the catalyst of finding out that her society is willing to kill her for the crime of not being able to fully conform. In all of these cases, the person is given incentive to rebel against their society.
This brings us to the other major component, which is the revolution. Once our hero and any of their friends have become outcasts, they eventually manage to play an important role in finding a better future. Metropolis does have a unique outcome in the way it ends with a compromise. Although Joh Fredersen is still presumably in charge of the city, he has to mediate with the working class in order to make things start working again. This joining together of the previously divided upper and lower classes suggests a better world for all.
The mediator between head and hands must be the heart... or is it the nervous system? I always get those two mixed up.
More recent dystopias seem to involve a much more violent revolution. Granted, things got pretty chaotic in the climax of Metropolis but the situation was ultimately resolved peacefully. We fast forward ahead to later dystopian movies and the authorities get much more vicious. The result ends up being that a peaceful solution is not possible, and the only hope is to overthrow the prevailing authority. In many cases the authorities aren't just negligent but also extremely dishonest, resulting in cases like The Running Man where the heroes ultimately seek to expose their treachery. Elysium involves multiple parties trying to gain control of the titular station for their own ends, but the only one with good intentions is the hero.
It's interesting as well to look at the much bleaker dystopian movies by contrast, as they seem to be less common. Blade Runner and Escape From New York both involve a gradually decaying society but there is never any real sign of improvement by the end. If anything things have only gotten worse in Escape From New York, with society collapsing even further and getting even darker by the time of Escape From L.A.. Blade Runner never really sees any drastic changes in society. Deckard is never fully satisfied with living in the crowded and pollution-choked world of his story but he more or less accepts it for what it is and just tries to get by.
It is curious that we don't see many bleaker dystopian films. Between The Hunger Games, Elysium, and Divergent, the genre has found a strange popularity in the present day, but you still don't see very many darker films, barring possible exceptions like District 9.