Emerging scenarios such as autonomous vehicles and the Internet-of-Things require large-scale cyber-physical systems (CPS), i.e., computing devices that interact with the physical world. To cope with their complexity, model-based design has long been advocated as a prominent approach for their rigorous development. However, the state of the art does not adequately account for two major issues: space, to capture the distribution of CPS devices as well as their mobility; and uncertainty, e.g., to reflect lack of knowledge about the environment, the accuracy of the model, or errors occurring in the real world. Our goal is to develop modelling and analysis techniques for CPS where space and uncertainty are first-class citizens. We envisage a component-based framework where digital and physical components have locality and mobility features, and where uncertainty is captured by means of probabilistically distributed activities to describe their dynamics. We devise a system to specify spatio-temporal CPS requirements, turning them into probabilistic spatio-temporal logical specifications that will be at the basis of efficient algorithms for the analysis, verification, and synthesis. We will apply our techniques to real case studies on smart buildings and crowd-navigating robots.