The intuition of emergence is that new properties, properties that make a causal difference in the world, can emerge in higher level organization. A realm of issues in which the metaphysical possibility (or impossibility) of emergence is focal is the realm of mental phenomena. Are minds - in particular, yours and mine - genuine emergents, with causal power in the world, or are they at best epiphenomena, with no consequence? I will argue that the simple intuition of emergence is roughly correct, but that it requires a very non-simple shift in underlying metaphysical framework in order to make sense of it. In particular, it requires a rejection of standard particle or substance metaphysical frameworks in favor of a process metaphysics.