Vortex shedding is of fundamental interest in fluid dynamics, with many applications in physics, engineering, and biology. Numerical studies of separated flows using the full governing equations are numerically expensive, and in practice, low order approximations such as point vortex or vortex sheet models are often used instead. These models are based on simple algorithms used to satisfy the Kutta condition at sharp edges. Here I will present highly resolved direct numerical simulations of flow past a flat plate that give insight into detailed aspects of the separation process. These benchmark results are used to evaluate the models and determine the extent to which they reproduce the flow. To conclude, I will present the fascinating dynamics observed for the simplest possible shedding model.