Inflection is the systematic relation between words’ morphosyntactic content and their morphological form; as such, the phenomenon of inflection raises fundamental questions about the nature of morphology itself and about its interfaces. Within the domain of morphology proper, it is essential to establish how (or whether) inflection differs from other kinds of morphology and to identify the ways in which morphosyntactic content can be encoded morphologically. A number of different approaches to modeling inflectional morphology have been proposed; these tend to cluster into two main groups, those that are morpheme-based and those that are lexeme-based. Morpheme-based theories tend to treat inflectional morphology as fundamentally concatenative; they tend to represent an inflected word’s morphosyntactic content as a compositional summing of its morphemes’ content; they tend to attribute an inflected word’s internal structure to syntactic principles; and they tend to minimize the theoretical significance of inflectional paradigms. Lexeme-based theories, by contrast, tend to accord concatenative and nonconcatenative morphology essentially equal status as marks of inflection; they tend to represent an inflected word’s morphosyntactic content as a property set intrinsically associated with that word’s paradigm cell; they tend to assume that an inflected word’s internal morphology is neither accessible to nor defined by syntactic principles; and they tend to treat inflection as the morphological realization of a paradigm’s cells. Four important issues for approaches of either sort are the nature of nonconcatenative morphology, the incidence of extended exponence, the underdetermination of a word’s morphosyntactic content by its inflectional form, and the nature of word forms’ internal structure. The structure of a word’s inventory of inflected forms—its paradigm—is the locus of considerable cross-linguistic variation. In particular, the canonical relation of content to form in an inflectional paradigm is subject to a wide array of deviations, including inflection-class distinctions, morphomic properties, defectiveness, deponency, metaconjugation, and syncretism; these deviations pose important challenges for understanding the interfaces of inflectional morphology, and a theory’s resolution of these challenges depends squarely on whether that theory is morpheme-based or lexeme-based.