Network models offer an efficient pore-scale approach to investigate transport in partially saturated porous materials and are particularly suited to study capillarity. Drying is a prime model application since it involves a range of physical effects: capillary pumping, viscous liquid flow, phase transition, vapor diffusion, heat transfer, but also cracks and shrinkage.This review article gives an introduction to this modern technique addressing required model input, sketching important elements of the computational algorithm and commenting on the nature of simulation results. For the case of drying, it is illustrated how network models can help analyze the influence of pore structure on process kinetics and gain a deeper understanding of the role of individual transport phenomena. Finally, a combination of pore network model and discrete element method is presented, extending the application range to mechanical effects caused by capillary forces.