This review is concerned with the structure, electrical, and optical properties of mixed-valence platinum complexes of the K$_2$ Pt(CN)$_1$, Br$_{0,30}$3H$_2$O type and of TTF-TCNQ salts. Special attention is paid to the experimental results on the anisotropy of electron motion in these quasi-one-dimensional crystals. The theory of the Peierls metal-insulator transition is considered for a one-dimensional system in the molecular field approximation, allowing for statistical fluctuations of the order parameter. It is shown that the Peierls transition is associated with the appearance of a giant Kohn anomaly in the phonon spectrum. The experimental results confirming the occurrence of the Peierls transition in platinum complexes (structure data, paramagnetic susceptibility, and phonon spectrum) are analyzed from the theoretical point of view. An analysis is also made of the influence of three-dimensional effects and of the disorder in crystals on the Peierls transition. The possibility of the Peierls transition in TTF-TCNQ is considered and the problem of the paraconductivity resulting from this transition is discussed.