Prosodic focus is often analyzed as flagging expressions for which alternative semantic meanings are salient in context. These alternative meanings can then compose pointwise, and play a crucial role in explaining contextual effects on prosodic prominence, but also constrain scalar implicatures, focus association, and related phenomena. This talk presents evidence that prosodic focus in fact relies on a syntactic mechanism of alternative generation. Focused constituents introduce a set of alternative expressions, which then 'project' in a pointwise way in syntax to generate sets of larger alternative expressions. Syntactic alternative projection sheds new light on a number of oddball phenomena, such as focus below the word level, metalinguistic uses of focus, expletive insertion within words, and echo questions, building the pioneering work on these phenomena by Artstein (2002). When looking at association with 'only" or scalar implicatures, however, it's not clear that these tap the same notion of alternatives. Instead, what we find looks more like semantic domain restriction.