Air motion representative of some of the flows past a moving car is studied, particularly in the gap between the car underbody (undertray, front flap or forewing) and the ground, using theory and computation. The ground-affected flows encountered are two- or three-dimensional, laminar, transitional or turbulent, and attached or separated. Given Reynolds numbers in the approximate range 1–10 million, emphasis here is placed first on key physical flow mechanisms: viscous-inviscid interaction filling either much or part of the gap; the generation of strong upstream influence; an abrupt pressure jump at the leading edge; the moving-ground condition; substantial diffuser flow reversals and wake effects; in three dimensions the distinguishing between inflow and outflow edges; and turbulent flow modelling. Second, for various underbody shapes, predictions are presented of the surface pressures and shear stresses, the lift or downforce, and the velocity profiles. Extensions of these to include edge effects, three-dimensionality and turbulence modelling are examined, along with optimization for certain shapes concerned with front-flap design and comparisons with recent experiments.