Interpretations that follow Everett's idea that (at some level of description) the universal wave function contains a multiplicity of coexisting realities, usually claim to give a completely local account of quantum mechanics. That is, they claim to give an account that avoids both a non-local collapse of the wave function, and the action at a distance needed in hidden variable theories in order to reproduce the quantum mechanical violation of the Bell inequalities. In this paper, I sketch how these claims can be substantiated in two renderings of Everett's ideas, namely the many-minds interpretation of Albert and Loewer, and versions of many-worlds interpretations that rely on the concepts of the theory of decoherence.