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Representational systems such as language, mind and perhaps even the brain exhibit a structure that is often assumed to be compositional. That is, the semantic value of a complex representation is determined by the semantic value of their parts and the way they are put together. Dating back to the late 19th century, the principle of compositionality has regained wide attention recently. Since the principle has been dealt with very differently across disciplines, the aim of the two volumes is to bring together the diverging approaches. They assemble a collection of original papers that cover the topic of compositionality from virtually all perspectives of interest in the contemporary debate. The well-chosen international list of authors includes psychologists, neuroscientists, computer scientists, linguists, and philosophers.