We investigate continuations in the context of idealized call-by-value programming languages. On the semantic side, we analyze the categorical structures that arise from continuation models of call-by-value languages. On the syntactic side, we study the call-by-value continuation-pas sing transformation as a translation between equational theories. Among the novelties are an unusually simple axiomatization of control operators and a strengthened completeness result with a proof based on a delaying transform. (C) 2003 Elsevier Inc. All rights reserved.