We have a conundrum. The physical basis of information is clearly a highly active research area. Yet the power of information theory comes precisely from separating it from the detailed problems of building physical systems to perform information-processing tasks. Developments in quantum information over the last two decades seem to have undermined this separation, leading to suggestions that information is itself a physical entity and must be part of our physical theories, with resource-cost implications. We will consider a variety of ways in which physics seems to affect computation, but will ultimately argue to the contrary: rejecting the claims that information is physical provides a better basis for understanding the fertile relationship between information theory and physics. Instead, we will argue that the physical resource costs of information processing are to be understood through the need to consider physically embodied agents for whom information-processing tasks are performed. Doing so sheds light on what it takes for something to be implementing a computational or information-processing task of a given kind.