Brian is the family pet.  He and Peter are best of friends and often hang out together.  Even though Brian is a dog, the entire family treats him as an equal (of course, the rest of society is not the same as seen when he runs away and tries to buy cigarettes. 

The entire family takes all their problems to Brian.  They rely on his advice which is usually pretty sound.  Brian's past, however, is somewhat a mystery.  He often talks of things he did in his past.  He hung out with Andy Warhol in the 70's and even helped Marissa Tome just to name a few.