In recent years, construction-based approaches to morphology have gained ground in the research community. This framework is characterized by the assumption that the mental lexicon is extensive and richly structured, containing not only a large number of stored words but also a wide variety of generalizations in the form of schemas. This review explores two construction-based theories, Construction Morphology and Relational Morphology. After outlining the basic theoretical architecture, the article presents an array of recent applications of a construction-based approach to morphological phenomena in various languages. In addition, it offers reflections on challenges and opportunities for further research. The review highlights those aspects of the theory that have proved particularly helpful in accommodating both the regularities and the quirks that are typical of the grammar of words. Expected final online publication date for the Annual Review of Linguistics, Volume 8 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.