Injustice can present in various shapes and sizes. There may be injustice at work place, at home or in your personal life. The only way to handle it is to fight it back using non-aggressive means.
First understand whether you are really a victim of injustice. Do an introspection of yourself and find out whether you were denied what you deserved. After all, your colleague who got the promotion may have truely worked hard to accomplish the position that he got; or your girlfriend may have found someone more caring and understanding than you had been to her.
After you are convinced that you did not deserved to be dumped it is time to take action.
Every action should begin with a dialogue. If you were denied a promotion at job talk to your boss what shortcomings were identified in you by the decision makers. If you did not get a convincing answer proceed to the next step.
Write an unofficial letter or email to your superiors expressing your utmost dissatisfaction with the decision. Enumerate causes why you thought you were the most eligible candidate for this position. Do not point fingers at the person who got this position. This could be misunderstood as your personal grudge with the person who got it and more people will sympathize with him rather than with you.
Involve more people in your office, but be passive. Try to gain sympathy from your colleagues. Many times the people who run the show care a lot about what the rest of the staff thinks about them, therefore any activity they think might potentially harm their reputation is taken seriously and many times they come to the negotiating table. But again, it all depends on how you propagate the message.
Write an official letter to people above those who made this decision. Detail in it why you think you were deserving a better treatment than this. Again, do not point fingers at any one. Furnish enough proof testifying that you have been really doing an excellent job. Enumerate instances where you proved to be superior to your colleagues.
Take legal action only if that is extremely necessary. Remember if you achieve finally what you wanted by a court order you may not like to work in a hostile environment that would be created at your work place because of that.