The computational modeling of the transition process characteristic of flows over swept wings is discussed. Specifically the crossflow instability and crossflow/T-S wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that regular stability theory is insufficient to explain the discrepancies between experiments and between theory and experiment (e.g. steady vs. unsteady, interactions, …). The leading edge region of a swept wing will be considered in a three-dimensional spatial simulation with random disturbances as the initial conditions.