Jason Peter Todd was born to a poor family. When he was 8 years old he was found stealing the tires off of the Batmobile. Batman found him doing this, so he tied him in a chair, took him home and had a long talk with him. When Batman took Jason home he discovered that Jason's family was killed. Batman adopted Jason and made him Robin.
As Robin, Jason often threatened Criminals, and almost killed some. Jason didn't really listen to Batman's orders. One day The Joker captured him and beaten to death with a crowbar. Batman could not save Jason in time. Jason Peter Todd was pronounced dead. Three years later a mysterious criminal started killing other criminals. He was dressed in a red hood. It was later discovered Jason was this criminal. After Jason died, Jason was found by a cloaked person who put him in the Lazurus pit. Jason came out screaming in pain. For three years Jason traveled the globe learning martial arts under an assumed name. This was how he became that criminal. Red Hood.
Jason then started to plot his revenge against Batman and so started the events of Batman: Under the Red Hood. At the end, Jason survived and decided to move to a different city, and at first wound up in Los Angeles where he rented an apartment under an assumed name and continued his criminal acts.