An ideal superlattice is an array of two (or more) alternating layers of materials with a single period, fixed barrier height and infinitely abrupt interfaces. A real superlattice differs from an ideal one in many aspects and this affects the band structure. They include unsharp interfaces, interface disorder, small fluctuations in thicknesses of quantum wells (barriers) and in the potential barrier heights from layer to layer. The band structure of superlattices in these realistic cases have been investigated. The relevance of these non-ideal cases to the shifting of the ground-state energy of the electrons, holes, and the effective energy gap are also discussed.