This article deals with a reputedly non-hierarchical relationship between dance - in particular site-specific contemporary dance and urban dance - and the space where such performances literally take place. It's a multifaceted connection between theoretical and empirical issues concerning the creation, the reception and the analysis of these performances. After describing from a genealogical point of view some specific roots mostly regarding the theatre (performing arts) but also the visual arts (performance art), some questions are raised. The first ones concern the way sociology has studied artistic performances and their own spaces, focusing on a body/urban space relationship. Other questions are then put on the conflicting textual side of performance, making reference both to semiotics and to performance studies. The second part of the contribution is dedicated to a thematic presentation, almost a sketched map, of some relevant case-studies that have been chosen just to show some peculiar configurations of this dance/space connection.