This article reviews the experimental and theoretical studies of the pinch effect in a solid-state plasma in the period 1958--1975. Different methods of observing the pinch effect and ways of initiating and suppressing this effect are described. Special attention is paid to the time evolution of this phenomenon. The fundamental features of the pinch effect in semiconductors under lattice-heating conditions are pointed out. The problems are discussed in detail of plasma stability in the pinch effect, as well as the mechanisms of breakdown of a pinch in a longitudinal magnetic field. The form of the recombination-radiation spectra in the pinch effect in a degenerate electron-hole plasma is analyzed. The fundamental experimental results from studying a $\theta$-pinch in InSb and Ge are given and analyzed. The applied aspects of studying the pinch effect in a solid-state plasma are pointed out, and unsolved problems are noted. Analogies are pointed out in a number of cases with the corresponding gas-discharge developments.