In this dissertation, I present a suite of studies investigating the neural and cognitive bases of semantic composition. First, I motivate why a theory of semantic combinatorics is a fundamental desideratum of the cognitive neuroscience of language. I then introduce a possible typology of semantic composition: one which involves contrasting feature-based composition with function-based composition. Having outlined several different ways we might operationalize such a distinction, I proceed to detail two studies using univariate and multivariate fMRI measures, each examining different dichotomies along which the feature-vs.-function distinction might cleave. I demonstrate evidence that activity in the angular gyrus indexes certain kinds of function-/relation-based semantic operations and may be involved in processing event semantics. These results provide the first targeted comparison of feature- and function-based semantic composition, particularly in the brain, and delineate what proves to be a productive typology of semantic combinatorial operations. The final study investigates a different question regarding semantic composition: namely, how automatic is the interpretation of plural events, and what information does the processor use when committing to either a distributive plural event (comprising separate events) or a collective plural event (consisting of a single joint event).