This article is mainly concerned with the analysis of methods of computation of spectral properties of solids. These properties cover a large variety of fields such as optical spectra of crystals, phonon effects in superconducting tunneling, infrared absorption, X-ray emission, dynamic magnetic susceptibilities, impurity modes, photoemission of electrons, phonon, electron and magnon densities of states, etc. A common feature of the calculation of all these properties is integration over the Brillouin zone. Five computational methods for performing this integration have evolved and have been applied so far. In this article these methods are analyzed for the first time on a general basis, and particular emphasis is put on resolution, accuracy and computing effort. Because of the very broad scope of the subject, a number of relevant problems of physical and computational nature are briefly introduced and discussed in a separate section.