Modern Hebrew exhibits a non-concatenative morphology of consonantal "roots" and melodic "templates" that is typical of Semitic languages. Even though this kind of non-concatenative morphology is well known, it is only partly understood. In particular, theories differ in what counts as a morpheme: the root, the template, both, or neither. Accordingly, theories differ as to what representations learners must posit and what processes generate the eventual surface forms. In this paper I present a theory of morphology and allomorphy that combines lexical roots with syntactic functional heads, improving on previous analyses of root-and-pattern morphology. Verbal templates are here argued to emerge from the combination of syntactic elements, constrained by the general phonology of the language, rather than from some inherent difference between Semitic morphology and that of other languages. This way of generating morphological structure fleshes out a theory of morphophonological alternations that are non-adjacent on the surface but are local underlyingly; with these tools it is possible to identify where lexical exceptionality shows its effects and how it is reined in by the grammar. The Semitic root is thus analogous to lexical roots in other languages, storing idiosyncratic phonological and semantic information but respecting the syntactic structure in which it is embedded. * Thanks to Alec Marantz, Maria Gouskova and Michael Becker for their input into Chapter 3 of my 2016 NYU dissertation, on which this paper is based. Thanks also to Edit Doron and Stephanie Harves for their guidance and comments, to Gillian Gallagher for helpful discussions, and to Maria once more for written comments on the manuscript. The ideas presented here benefited greatly from conversations with Hagit Borer,