In this book, Derk Pereboom explores how physicalism might best be formulated and defended against the best anti-physicalist arguments. Two responses to the knowledge and conceivability arguments are set out and developed. The first exploits the open possibility that introspective representations fail to represent mental properties as they are in themselves; specifically, that introspection represents phenomenal properties as having certain characteristic qualitative natures, which these properties might actually lack. The second response draws on the proposal that currently unknown fundamental intrinsic properties provide categorical bases for known physical properties and would also yield an account of consciousness. While there are non-physicalist versions of this position, some are amenable to physicalism. The books third theme is a defense of a nonreductive account of physicalism. The type of nonreductivism endorsed departs from others in that it rejects all token identity claims for psychological and microphysical entities. The deepest relation between the mental and the microphysical is constitution, where this relation is not to be explicated by the notion of identity.