This chapter identifies what the authors believe to be the core computational primitives that underlie phonological knowledge. It presents evidence from the domain of cognitive neuroscience that attempts to investigate the nature of the neural correlates of these primitives. Phonological grammars provide a framework for how speech sounds are represented and the nature of the various combinatorial operations they undergo in mapping between lexical representations and their surface-forms. Traditionally, generative phonology has asked two questions: (1) what representations subserve phonology (e.g., features, segments, syllables) and (2) what procedures map between surface forms and memory representations. The only language-specific circuits motivated by classic phonetic and phonological theory are those needed to represent language-specific phonetic and phonological primitives in long-term memory. The chapter focuses on the nature of phonological representations, the primitives that have been investigated to date in the cognitive neuroscience literature.