This talk describes some personal highlights of my academic career, involving a mix of theoretical and applied topics, and lots of collaboration. My research interests focus on the development and application of stochastic models, often in space-time. For applications, the emphasis is on mechanistic models that reflect underlying physical processes, albeit in highly simplified form. Such models bring insight and understanding of these processes and enable control strategies to be investigated. My early research concentrated mainly on theoretical work on point processes, which has informed later work on applications in two distinct areas. In the life/medical sciences, I have concentrated particularly on population processes and epidemics involving a range of transmissible diseases. Transmission on structured populations has led to work with random networks and more generally to communications applications involving the spread of information. In parallel, I have developed models for processes arising in the physical sciences and particularly in hydrology where rainfall and soil moisture are the main examples. The talk will cover a selection of generic models and applied problems.