You've opened the broadest possible topic, Cayla, and we can only begin to approach it here. Usually the two (ΕΡΩΣ, love/desire and ΘΑΝΑΤΟΣ, death) are juxtaposed as opposites. For early Greek philosophers, eros was often conceived as the creative life force, the origin of all things, even of all gods. For Aristotle, eros as "appetite" was the source of all movement in the universe. For Freud, it was the force that sustained life as well as the health of the mind.
Thanatos promotes the opposite: it is the negation of eros and of life itself. Freud spoke of the Todestrieb, the "death drive" or "death instinct" that is responsible for neurosis, psychosis, and all self-destructive, life-negating behavior. For a fascinating introductory read on all this, try Norman O. Brown's Life against Death, a psychoanalytical account of the interaction of eros and thanatos throughout history. And watch this thread for further developments!