The current experimental data and theoretical views on structural transitions with formation of chargedensity waves (CDW) in layer compounds of transition-metal dichalcogenides are reviewed. The crystallographic data on the parameters of the incommensurate 1$T$ and 2$H$ modifications are discussed, together with the information on the change in these parameters in transitions to the commensurate state. A microscopic interpretation of the CDW transitions is based on a model of nested regions of the Fermi surface for the 1$T$ modification and a saddle-point model for the 2$H$ compounds. The fundamental characteristics of transitions from a normal metal to an incommensurate CDW state and from the incommensurate to the commensurate state (change in the period of the superstructure in the layer and perpendicular to the layers) are described on the basis of the phenomenologtcal Ginzburg--Landau theory. Experimental data on changes in the phonon spectrum and the effect of impurities on CDW transitons are also treated.