We establish a systematic correspondence between sequent and resolution calculi for a broad class of modal logics. Our main result is that soundness and completeness transfer from sequent to resolution calculi as long as cut and weakening are admissible. We first construct generative calculi that essentially import modal rules to a resolution setting, and then show how soundness and completeness transfer to absorptive calculi, where modal rules are translated into generalised resolution rules. We discuss resolution calculi that establish validity, and then introduce local clauses to generate calculi for inconsistency. Finally, for modal rules of a certain shape, we show how to construct layered resolution calculi, a technique that has so far only been established for the modal logic K. Our work directly yields new sound and complete resolution calculi, and layered resolution calculi, for a large number of modal logics.