Calculations of exciton energies in single quantum wells and in superlattices are described. The results show that for most well widths the exciton remains essentially three-dimensional (3D) -like. The exciton binding energy as a function of well width has a peaked structure with the maximum binding energy occurring at larger well widths in a superlattice structure compared with the finite well. Furthermore the magnitude of the binding energy is typically several meV larger for finite wells than for superlattices. It is shown that in magnetic superlattices the Zeeman splitting of the exciton can be used to advantage to determine band offsets for small (<30%) percentage offsets in the valence band.