If you ate your pet in your dream, then you are frightened about your own natural instincts and desires.
If you saw your or someone else’s pet in your dream it could signify your ability to hold your temper and exercise self-control. You are keeping your uncivilised behaviours in check for the sake of those around you.
On the other hand, it could mean that you crave love and acceptance from other people. It’s possible you lack this from those in your life and feel neglected as a result. It is common when someone is infatuated with another that they will dream about pets – do you have a deep admiration for someone in your waking life?
If you dream about a pet that died, then your subconscious is helping you to mourn the loss and help you to heal. If you dream about a pet that you had many years ago, consider the time in your life when you had it. Perhaps you miss something about that period that you want back.
A situation in your current life might be similar to that of a time when you had a pet, so you are connecting the two in your dreamscape. Can you learn anything from the first time it happened and apply it to the present?
On the flipside, maybe there is something from your past that is still haunting you and you need to resolve it before you can move on.
Consider what the pet was like; perhaps you want to embody some of the traits of the animal you saw, such as gracefulness, boldness or kindness.
If your pet escaped then the dream could be convincing you to express some of your innermost urges. If you cannot suppress them any longer it might be time to just let them out.