This paper explores the relationship between several ideas about the mind and cognition. The hypothesis of extended cognition claims that cognitive processes can and do extend outside the head, that elements of the world around us can actually become parts of our cognitive systems. It has recently been suggested that the hypothesis of extended cognition is entailed by one of the foremost philosophical positions on the nature of the mind: functionalism, the thesis that mental states are defined by their functional relations rather than by their physical constituents. Furthermore, it has been claimed that functionalism entails a version of extended cognition which is sufficiently radical as to be obviously false. I survey the debate and propose several ways of avoiding this conclusion, emphasizing the importance of distinguishing the hypothesis of extended cognition from the related notion of the extended mind.