Tangible and Embodied interactions are areas of research within HCI and Interaction design. They refer to a way in which interacting with computer systems is closer to the way we interact with the real world. Instead of using devices such as a computer or a phone, we interact using seemingly non-technological objects, by moving our bodies or by using gestures. Since the early 2000s, tangible and embodied interactions have been applied and researched also in Cultural Heritage and museums, in an attempt to overcome issues induced by screen-based devices that may disengage visitors from the objects, their materiality and the physicality of the visit. This article surveys tangible and embodied interactions in museums, over a period of two decades since 2000. Over 120 projects have been researched and analysed thematically to provide a categorization based on cultural communication, interaction features and museological aspects. This categorization offers a conceptualization of tangible and embodied interactions in museums and Cultural Heritage; it suggests a terminology to describe the design characteristics of tangible and embodied interaction interventions, therefore facilitating the orientation of future research efforts in the field.