The development of wireless sensor networking, social networking, and wearable sensing techniques has advanced the boundaries of research on understanding social dynamics. Collaborative sensing, which utilizes diversity sensing and computing abilities across different entities, has become a popular sensing and computing paradigm. In this paper, we first review the history of research in collaborative sensing, which mainly refers to single space collaborative sensing that consists of physical, cyber, and social collaborative sensing. Afterward, we extend this concept into cross-space collaborative sensing and propose a general reference framework to demonstrate the distinct mechanism of cross-space collaborative sensing. We also review early works in cross-space collaborative sensing, and study the detail mechanism based on one typical research work. Finally, although cross-space collaborative sensing is a promising research area, it is still in its infancy. Thus, we identify some key research challenges with potential technical details at the end of this paper.