We present an accurate theory for the excitonic absorption in quantum-well structures which yields very good agreement with a wide range of experimental data. Our approach is based on an expansion of the exciton wave function in terms of multicomponent envelope functions of electron and hole states. It is rather general with respect to band-structure effects and potential profiles. In momentum space the two-particle Schrödinger equation becomes a set of coupled integral equations for the expansion coefficients which we solve by means of a modified quadrature method. Our calculations reproduce all the essential details of a great variety of experimental spectra from high-quality GaAs-Al x Ga 1− x As quantum-well structures. We demonstrate that this requires one to take into account both band-structure effects (HH-LH coupling and nonparabolicity) and the coupling of different electron-hole subband pairs caused by the Coulomb interaction. These effects strongly modify the peaks in the exciton continuum which correspond to Fano resonances. Moreover, the Coulomb coupling of subband pairs is often so substantial that it is not possible to attribute excitons to a single subband pair. The free electron-hole absorption coefficient can have pronounced Van Hove singularities which disappear in the excitonic absorption spectrum. Thus, in contrast to bulk semiconductors, the Coulomb interaction can decrease the absorption coefficient at the fundamental absorption edge.