This paper summarizes research performed over the past decade on the direct molecular simulation of dilute gas flows. Similar to the molecular dynamics method, a potential energy surface is the sole model input to a direct molecular simulation calculation. However, instead of simulating the motion of all atoms in the system deterministically, the direct molecular simulation method uses stochastic techniques and assumptions, adopted from the well-established direct simulation Monte Carlo method, which are accurate for dilute gases. Using the same potential energy surface as input, the direct molecular simulation method is verified to exactly reproduce pure molecular dynamics results for shock-wave flows. The direct molecular simulation method is then used to investigate nonequilibrium flows such as strong shock waves and dissociating nitrogen systems involving rotation–vibration coupling and coupling between internal energy and dissociation. Direct molecular simulation algorithms are detailed, and a number of new results relevant to hypersonic flows are presented along with a summary of other recent results in the literature.