When we use language, we draw on a finite stock of lexical and functional meanings and grammatical structures to assign meanings to expressions of arbitrary complexity. According to the Principle of Compositionality, the meanings of complex expressions are a function of constituent meanings and syntax, and are generated by the recursive application of one or more composition operations. Given their central role in explanatory accounts of human language, it is surprising that relatively little is known about how the brain implements these composition operations in real time. In recent years, neurolinguistics has seen asurge of experiments investigating when and where in the brain meanings arecomposed. To date, however, neural correlates of composition have not been firmly established. In this article, we focus on studies that set out to find the correlates of linguistic composition. We critically examine the paradigms theyemployed, laying out the rationale behind each, their strengths and weaknesses. We argue that the still blurry picture of composition in the brain may be partly due to limitations of current experimental designs. We suggest that novel and improved paradigms are needed, and we discuss possible next steps in this direction. At the same time, rethinking the linguistic notion of composition, as based on a tight correspondence between syntax and semantics, might be in order.