Physicalist theories are either reductive or non-reductive. I argue that two of the reductive theories, eliminativism and the identity theory, do not succeed. My point is that if we were to use a physical description of the brain to explain behavior, we must be able to individuate brain states in terms of mental states. Human actions are most often defined in terms of intentional states. The other reductive physicalist theory, the identity theory, seems to be supported by some recent experiments. However, the multiple-realization argument is considered as a devastating argument against any kind of identity between the mind and the brain. Nevertheless, I believe that this argument is flawed, but that the identity theory is nevertheless inadequate for other reasons. In the end, I present but dismiss a structural identity theory as an alternative to the classical identity theory.