Nowadays the computing technology is integrated in all aspects of daily and professional lives. Such integration creates what is called cyber-physical systems (or, preferred by communication engineers, the Internet of Things). Such systems combine both physical components which are modeled by continuous paradigms such as differential equations and computing elements which are inherently discrete. This continuous/discrete combination creates tremendous challenges, both from the theoretical as well as practical applicability. In this talk we give an introduction to a part of computability theory, called computable analysis, which has been developed to address issues of computability over continuous domains. We show one application of such approach in the complexity-theoretic analysis of the reachability problem in dynamical systems.