Boas (1917) mentioned several phenomena found in the morphosyntax of Amerindian languages (including nominal incorporation and lexical affixation) that posed challenges to accepted views of synchronic and typological issues raised by genealogical relatedness and areal convergence on the continent, morpheme classes like roots, stems, and affixes in languages in general, and whether the fundamental unit of human speech is the word or the sentence. A century later, and despite the increased amount of data available and a substantial amount of theorizing on morphosyntactic issues, these challenges have proved considerably recalcitrant. Framed in terms of morpheme types, word domains, and word classes, this article surveys the progress since Boas’s introductory paper and examines open questions in the study of the morphosyntax of indigenous languages of the Americas.