The present state of the theory and the main experimental results are reviewed for systems in which the antiferromagnetic ordering is directly due to a peculiar topology of the Fermi surface, i.e., to the presence of nested electron and hole sheets. A familiar example of such a system is chromium, which supports a spin-density wave (SDW) that is incommensurate with the lattice. For this reason much of the experimental material discussed in this review is for chromium and its alloys with transition and nontransition metals. The theoretical description of SDWs of this type is based on the excitonic insulator model, which is discussed in detail not only in connection with the phase diagrams and SDW structure but also in regard to the electronic properties of systems of this type (measurements of the de Haas-van Alphen effect, optical measurements, band-structure calculations from first principles, etc.). The review concludes with a discussion of less-studied transition-metal compounds which apparently also support a SDW state due to a peculiar topology of the Fermi surface.