'Moving sites' investigates relationships between site-specificity and what has been termed a 'new mobilities paradigm' in the social sciences. As the social sciences develop increasingly sophisticated theorizations of what it means to be mobile, site-specific performance is well placed to investigate how we understand and experience our mobility. Given the emphasis on the very 'specificity' of site-based theatre, models for theorizing it have usefully drawn on ideas such as locatedness, sense of place, emplacement, and the local in relation to the global. And yet there is also a growing context for thinking about site work in relation to mobility. This article discusses works - by Mike Kelley, Mick Douglas, and National Theatre Wales - that not only enact conceptions of place as fundamentally tied up with questions of mobility, but also taken together begin to mark out a much broader disciplinary unhinging of site-based practice than has sometimes been imagined. Drawing on the richness and complexity of mobile practices as they are investigated in the social sciences, the article deliberately focuses on site-specific performances that offer an alternative version of mobility to walking practices. The aim is to open new spaces for debate about the developing relationship between site and mobility.