If someone behind you is chasing you, it means something from the past still has a power over you today. While you may feel you are past it, the dream shows that you are still expending energy trying to get distance between you and it. The feeling that comes up in dreams like this is the key. The dream is attempting to show you that there is a link between the past trauma and that feeling today. If a parent is chasing you, it means that you still have issues with that parent today.
If you dream you're chasing someone, consider the context.For example, if you're angry at the person you're chasing, the chasing may represent a desire to act out on your anger towards that person.Chasing someone who has stolen something from you can represent your desire to set right a situation where you feel someone has taken advantage of you. If you are playfully chasing someone you like, it could represent your desire to interact with them or your fond feelings toward them.