Wh-phrases in English have two important properties: first, they can appear both raised and in-situ; second, while in-situ wh-phrases can take semantic scope beyond the immediately enclosing clause, raised ones cannot. I present a denotational semantics of interrogatives that naturally accounts for these two properties; it neither conducts movement at a level of semantic representation separate from surface syntax nor posits lexical ambiguity between raised and in-situ occurrences of the same wh-phrase. My analysis is based on the concept of continuations; in particular, it uses a novel type system for higher-order continuations to handle wide-scope wh-phrases while remaining within a Montague-style framework of grammar. This treatment sheds light on the combinatorics of interrogatives as well as other kinds of so-called A -movement.