The management of health data, from their gathering to their analysis, arises a number of challenging issues due to their highly confidential nature. In particular, this dissertation contributes to several security and privacy challenges within the smart health paradigm. More concretely, we firstly develop some contributions to context-aware environments enabling smart health scenarios. We present an extensive analysis on the security aspects of the underlying sensors and networks deployed in such environments, a novel user-centred privacy framework for analysing ubiquitous computing systems, and a complete analysis on the security and privacy challenges that need to be faced to implement cognitive cities properly. Second, we contribute to process mining, a popular analytical field that helps analyse business processes within organisations. Despite its popularity within the healthcare industry, we address two major issues: the high complexity of healthcare processes and the scarce research on privacy aspects. Regarding the first issue, we present a novel process discovery algorithm with a built-in heuristic that simplifies complex processes and, regarding the second, we propose two novel privacy-preserving process mining methods, which achieve a remarkable trade-off between accuracy and privacy. Last but not least, we present some smart health applications, namely a context-aware recommender system for routes, a platform supporting early mobilization programmes in hospital settings, and a health-oriented geographic information system. The results of this dissertation are intended to help the research community to enhance the security of the intelligent environments of the future as well as the privacy of the citizens regarding their personal and health data.