[en] This review deals with the properties of superconductors with competing electron spectrum instabilities, namely, charge-density waves (CDWs) and spin-density waves (SDWs). The underlying reasons of the electron spectrum instability may be either Fermi surface nesting or the existence of Van Hove saddle points for lower dimensionalities. CDW superconductors include layered dichalcogenides, NbSe₃, and compounds with the A15 and C15 structures among others. There is much evidence to show that high-T_c oxides may also belong to this group of materials. The SDW superconductors include URu₂Si₂ and related heavy-fermion compounds, Cr-Re alloys and organic superconductors. We review the experimental evidence for CDW and SDW instabilities in a wide range of different superconductors, and assess the competition between these instabilities of the Fermi surface and the superconducting gap. Issues concerning the superconducting order parameter symmetry are also touched upon. The accent is put on establishing a universal framework for further theoretical discussions and experimental investigations based on an extensive list of available and up-to-date references. (author)