This is a proposal for a 30 minute talk. In this talk, I will present and develop a new perspective on continuations: just as higher-order functions give you exponentials, higher-order continuations give you coexponentials. Using this perspective, I will show how to: (1) derive the classical control operators from coexponentials, (2) use coexponentials to encode common patterns of programming with continuations, (3) recover the well-known computational interpretation of classical logic using continuations, (4) define a language that combines exponentials and coexponentials without degeneracy.