This article examines the changing relationship between museums and heritage using a number of Dutch cases. It argues that if heritage was once defined as being museological in character, this order of precedence is under revision as museums themselves are recursively transformed by heritage dynamics. Such dynamics include the display of renovation work-in-progress; the enhancement of historical collections by relocation to prominent new sites and buildings; the transformation of old industrial sites into new art and public spaces; and a mutual reinforcement between the urban landscape setting and the institutions that compose it by virtual means. Postcolonial heritage practices worldwide enfold museums in a further set of transformatory dynamics: these include claims on cultural property that was removed in colonial times, but also the strategic transformation of cultural property into heritage for didactic purposes. Museums are subject to the recursive dynamics of heritage, which are turning them inside out.