The morpheme was the central notion in morphological theorizing in the 20th century. It has a very intuitive appeal as the indivisible and invariant unit of form and meaning, a minimal linguistic sign. Ideally, that would be all there is to build words and sentences from. But this ideal does not appear to be entirely adequate. At least at a perhaps superficial understanding of form as a series of phonemes, and of meaning as concepts and morphosyntactic feature sets, the form and the meaning side of words are often not structured isomorphically. Different analytical reactions are possible to deal with the empirical challenges resulting from the various kinds of non-isomorphism between form and meaning. One prominent option is to reject the morpheme and to recognize conceptually larger units such as the word or the lexeme and its paradigm as the operands of morphological theory. This contrasts with various theoretical options maintaining the morpheme, terminologically or at least conceptually at some level. One such option is to maintain the morpheme as a minimal unit of form, relaxing the tension imposed by the meaning requirement. Another option is to maintain it as a minimal morphosyntactic unit, relaxing the requirements on the form side. The latter (and to a lesser extent also the former) has been understood in various profoundly different ways: association of one morpheme with several form variants, association of a morpheme with non-self-sufficient phonological units, or association of a morpheme with a formal process distinct from affixation. Variants of all of these possibilities have been entertained and have established distinct schools of thought. The overall architecture of the grammar, in particular the way that the morphology integrates with the syntax and the phonology, has become a driving force in the debate. If there are morpheme-sized units, are they pre-syntactic or post-syntactic units? Is the association between meaning and phonological information pre-syntactic or post-syntactic? Do morpheme-sized pieces have a specific status in the syntax? Invoking some of the main issues involved, this article draws a profile of the debate, following the term morpheme on a by-and-large chronological path from the late 19th century to the 21st century.