Nowadays, it has become almost a matter of course to say that human mind is like a computer. Folks in all walks of life talk of ‘programming’ themselves, ‘multi-tasking’, running different ‘operating systems’, and sometimes of ‘crashing’ and being ‘rebooted’. Few who have used computers have not been touched by the appeal of the idea that our inner workings somehow resemble computing machines. The success of modern day computational psychology appears to bears witness to the explanatory and predictive pay-off in positing a connection between computers and minds. Among its other virtues, the computational framework has rendered theorising about inner processes respectable, it has provided a unified and naturalistic arena in which to conduct debates about psychological models, and it provides the tantalising possibility of accurately simulating and reproducing psychological processes. There is almost universal agreement that the mind is in some sense like a computer. But consensus quickly ends once we ask how the mind is supposed to be like a computer. Even after more than thirty years of model building, and a wealth of empirical work, surprisingly little consensus exists in cognitive science on the correct answer to this question. What is more, disagreement tends to lie at a relatively deep level. There is little agreement about the content of the notion of computation, what it means for a physical system, like the brain, to implement a computation, the broad-brush computational architecture of the mind, or how computational models fit with other models of the mind, such as control theoretic models, statistical models, or dynamical systems theory.