Physicalism – or roughly the view that the stuff that physics talks about is all the stuff there is – has had a popular press in philosophical circles during the twentieth century. And yet, at the same time, it has become quite fashionable lately to believe that the mind matters in this world after all and that psychology is an autonomous science irreducible to physics. However, if (true, downward) mental causation implies non-reducibility and Physicalism implies the converse, it is hard to see how these two views could be compatible. This paper reviews some classical arguments purportedly showing how the autonomy of the special sciences can be upheld without violating the laws of physics or the principle that physics constitutes a complete and closed system. These arguments are presented in order of increasing strength, indicating how the more popular arguments in fact fall short of establishing anti-reductionism of the intended kind. New arguments are added which claim to demonstrate quite effectively how downward causation is possible compatibly with the reign of physics. The paper begins with a section which distinguishes various kinds of reductionism.