The electronic structures of many materials can be well described by the one-particle picture within the band theory. A quantitative evaluation of band gaps in semiconductors and insulators, however, needs special care because the subtle balance between the exchange and correlation effects must be properly taken into account. This article reviews theoretical approaches for calculating band gaps of materials based on 1) many-body perturbation theory, 2) density-functional theory, and 3) wavefunction-based theory, and the advantages and of each theory disadvantages are discussed.