We argue that neural processes are neither analog nor digital computations; they constitute a third kind of computation. Analog computation is the processing of continuous signals; digital computation is the processing of strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike rates, are graded like continuous signals but are constituted by discrete elements (spikes); thus typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. This has three important consequences. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non-neural notions of computation ought to be replaced or reinterpreted in terms of neural computation.