The standard view of the form-meaning interfaces, as embraced by the great majority of contemporary grammatical frameworks, consists in the assumption that meaning can be associated with grammatical form in a one-to-one correspondence. Under this view, composition is quite straightforward, involving concatenation of form, paired with functional application in meaning. In this book, we discuss linguistic phenomena across several grammatical sub-modules (morphology, syntax, semantics) that apparently pose a problem to the standard view, mapping out the potential for deviation from the ideal of one-to-one correspondences, and develop formal accounts of the range of phenomena. We argue that a constraint-based perspective is particularly apt to accommodate deviations from one-to-many correspondences, as it allows us to impose constraints on full structures (such as a complete word or the interpretation of a full sentence) instead of deriving such structures step by step. Most of the papers in this volume are formulated in a particular constraint-based grammar framework, Head-driven Phrase Structure Grammar. The contributions investigate how the lexical and constructional aspects of this theory can be combined to provide an answer to this question across different linguistic sub-theories.