 The problem of computational implementation may be formulated in a couple of different ways. Platonists interpret the formalisms of computability theory as defining abstract objects. According to this interpretation, TMs, algorithms, and the like are abstract objects. But how can a concrete physical system implement an abstract object, and what precisely is this implementation relation? Anti-platonists treat the formalisms of computability theory simply as abstract computational descriptions. But how can a concrete physical system satisfy an abstract computational description? Regardless of how the problem of computational implementation is formulated, solving it requires an account of concrete computation—an account of what it takes for a physical system to perform a given computation.