Papermaking flows are extremely challenging for modeling and simulation, if one accepts their full complexity. A wide range of particles, including fibers, fiber fragments (fines) and fillers (non-organic particles), flow and interact with each other in a nondilute suspension, a complex geometry and at a high flow rate. Different simulation approaches are reviewed from particle-level simulations, through mesoscale simulations to the full flow geometry of the papermaking line. Their application to papermaking and potential to provide fundamental understanding as well as direct process-optimization support are discussed.