Everett's interpretation of quantum mechanics was proposed to avoid problems inherent in the prevailing interpretational frame. It assumes that quantum mechanics can be applied to any system and that the state vector always evolves unitarily. It then claims that whenever an observable is measured, all possible results of the measurement exist. This notion of multiplicity has been understood in different ways by proponents of Everett's theory. In fact the spectrum of opinions on various ontological questions raised by Everett's approach is rather large, as we attempt to document in this critical review. We conclude that much remains to be done to clarify and specify Everett's approach.

References added; clarifications; changes in section 4; forthcoming in SHPMH