They are both gifted vampires and members of the Olympic coven.
Their Life and Death counterparts are Archie Cullen and Jessamine Hale.
They introduce themselves to Bella when she visits their home for the first time, after Edward started dating her.
Jasper and Alice take Bella to Phoenix to hide from the tracker, James.
Jasper does his best to calm her down while Alice tries to foresee James's plans and sees Bella and James at Bella's old ballet studio.
A few years later, Peter came back for Jasper to tell him about life up in the North.
Jasper's skills and gift allowed him to gain command over the army in the Southern vampire wars, and he befriended another vampire called Peter who was allowed to live by Maria.
But Peter ran off with another newborn called Charlotte whom he was in love with.
This persuaded him to leave the army and lived with them until he became emotionally depressed by the pain of his prey and wandered off on his own.
He tried to kill as little as possible, but the thirst always won.