The Buddhist concept of anatta, when linked with the affective dimension of compassion, is to me the crown of Buddhism. By exposing the transparency of self, one opens up to the relational nature of identity, and thereby creates the ground for empathy and engagement.
Mahayana Buddhism speaks of two kinds of anatta, the non-self of the person and the non-self of things or dhammas. From the Tibetan Buddhist point of view the concept of shunyata or emptiness is simply anatta applied to phenomena. Nonetheless, in Tibetan Buddhist practice, when you do meditations on shunyata you start by analyzing your personal identity, just as you do in the Theravada tradition. In practical terms, that is where you must begin, because one’s own identity is the central attachment. It is the ontological sense of who you are that is the base for all subsequent projections of self identity.
The Mahayana takes the concept of anatta and extends that to the development of compassion for all things, since there really is no separation between self and other. An image that conveys this most beautifully is Shantideva’s concept of the entire world being comparable to a single organism, a body. He says that just as when the foot is in pain, the hand will spontaneously reach out to assuage the pain of the foot, in the same way—if you are no longer inhibited by self-centeredness—you will spontaneously reach out to assuage the pain of others. That metaphor beautifully conveys the central insight of Mahayana Buddhism: Once the self is seen through, it does not just mean liberation, but also that your spontaneous response to others becomes that of a profound empathy. You recognize that who you are is not because of some kind of metaphysical substance or essence that is tucked away inside you somewhere, but rather is determined by the unrepeatable matrix of relationships that constitute your own history.