The chapter describes two categories of process-based models, namely, hydrological and socio-hydrological models. It starts with an explanation of the modelling chain from climate drivers via process-based models to identification of hydrological and socio-hydrological drought characteristics. Then, the first category of process-based models is introduced, that is, hydrological models, which are divided in three types: spatially lumped, semi-distributed and spatially distributed models. Spatially distributed models are further subdivided based on whether they simulate lateral groundwater flow (GWfl) or not (nGWfl). An example model of each of these three types, including an application is given, that is, HBV (spatially lumped, semi-distributed), PCR-GLOBWB (spatially distributed model, nGWfl) and SIMGRO (spatially distributed model, GWfl). The second category of process-based models, that is, the socio-hydrological models, is also divided into three types: coupled-component, system-dynamics and agent-based models. The chapter addresses calibration and validation of process-based models and concludes with some guidance on how to select an adequate model, considering also the associated uncertainty.