What are the psychological, computational and neural underpinnings of language? Are these neurocognitive correlates dedicated to language? Do different parts of language depend on distinct neurocognitive systems? Here I address these and other issues that are crucial for our understanding of two fundamental language capacities: the memorization of words in the mental lexicon, and the rule-governed combination of words by the mental grammar. According to the declarative/procedural model, the mental lexicon depends on declarative memory and is rooted in the temporal lobe, whereas the mental grammar involves procedural memory and is rooted in the frontal cortex and basal ganglia. I argue that the declarative/procedural model provides a new framework for the study of lexicon and grammar.