Indefinites loom large in linguistic theorizing about scope, binding, and even basic architectural issues (e.g. the nature of the syntax-semantics interface and what sorts of objects sentences should denote). Two properties are especially striking: indefinites can poke their heads out of scope islands ('exceptional scope') and semantically bind non-maximally interpreted pronouns they don't--and can't--syntactically bind ('donkey anaphora'). Yet a unified picture of indefiniteness remains elusive. Theories of exceptional scope both over- and under- generate and turn out to be incompatible with theories of donkey anaphora (and vice versa). Against this backdrop, I'll argue that (a) dynamic and alternative/inquisitive semantics for indefinites, indefiniteness, and disjunction, though in some sense incompatible, are in fact intimately connected; (b) the computer science technique of continuations helps us bridge the gap and forge a new semantics encompassing both perspectives; and (c) this theory offers progress on a number of recalcitrant puzzles, and makes a number of novel predictions that are confirmed. Along with (exceptional) scope-taking and (dynamic) binding, data will be drawn from ellipsis, disjunction, distributivity, and maximal set anaphora. I'll argue that the class of exceptional scope-takers coincides with the class of externally dynamic operators; in other words, we can read an XP's exceptional scope properties off the way it semantically binds pro-forms it doesn't syntactically bind (and vice versa).