Achieving greater speeds and densities in the post-Moore’s Law era will require computation to be more like the physical processes by which it is realized. Therefore we explore the essence of computation, that is, what distinguishes computational processes from other physical processes. We consider such issues as the topology of information processing, programmability, and universality. We summarize general characteristics of analog computation, quantum computation, and field computation, in which data is spatially continuous. Computation is conventionally used for information processing, but since the computation governs physical processes, it can also be used as a way of moving matter and energy on a microscopic scale. This provides an approach to programmable matter and programmed assembly of physical structures. We discuss artificial morphogenesis, which uses the formal structure of embryological development to coordinate the behavior of a large number of agents to assemble complex hierarchical structures. We explain that this close correspondence between computational and physical processes is characteristic of embodied computation, in which computation directly exploits physical processes for computation, or for which the physical consequences of computation are the purpose of the computation.