This review paper was written on the occasion of the 40 th anniversary of the Drying Technology Journal. Interestingly, most of the progress made in the domain of drying modeling and simulation has occurred over the last 40 years. Indeed, 40 years ago, the comprehensive formulation of coupled heat and mass transfer in porous media was available, however its potential use for computational simulation was only in its nascent stage. This is therefore an ideal time span in which to take a full historical context, to present the state-of-the-art and to give insights into its future trajectory. All aspects are deliberately presented in a pedagogical manner with many illustrations to make the text accessible to young scientists. However, for the benefit of experts, detailed formulations are provided in the annexes. The main points addressed in this work include: • The description of the comprehensive macroscopic formulation, • An historical perspective of the progress made in computational simulation, • The contribution of modeling in parameter characterization, • The mechanical aspects of drying: strain and stress induced by drying, including the case of large deformations, • The impact of non-local equilibrium, • The promising domain of the digital twin in parameter tuning and control/command.