With the expanding applications of the simulated moving bed (SMB) chromatography technology in various industries, it becomes increasingly significant to systematically investigate SMB process modeling, simulation, and model-based control design. How to control an SMB process effectively is a significant and challenging problem at the frontier of process systems engineering research as well as industrial operation. Addressing the challenges in this area, this paper reviews recent advances in modeling and simulation of SMB separation processes and also clearly identifies the limitation of the existing modeling techniques in industrial applications. To facilitate SMB process modeling, the paper analyses the structure of the existing models for a better understanding of the functionality and suitability of each model. It is our belief that the effort on model development for process control can be made in two aspects: obtaining the sufficiently accurate model with simple representation and good robustness, and development of computationally efficient algorithms for solving the model equations which ultimately capture the process dynamics. Case studies are carried out to demonstrate the key concepts of process modeling and numerical solution of the models. The wavelet-based methods that we recently investigated are highlighted.