The terahertz (THz) range is the next frontier of electronics and optoelectronics with potential applications ranging from imaging, space communications, computing, quality control, and homeland security to biotechnology and medicine. At THz frequencies, the electron inertia becomes important, providing delay between the applied voltage and electron velocity and current. When the electron collisions with impurities and lattice vibrations are infrequent, this delay leads to oscillations of the electronic density (called plasma waves) with the transistor channels serving as resonant cavities for the plasma waves. In the collision-dominated regime, the plasma waves are overdamped but still play a role by dramatically changing the electron distribution in the device channels at THz frequencies. The resonant regime can be used to generate THz radiation. Both resonant and overdamped plasma waves enable other THz electronic devices, such as detectors, mixers, and phase shifters. Periodic (symmetrical and asymmetric) plasmonic structures are especially promising for generation and detection of THz radiation. In this article, we review the state of the art of the plasma-wave electronics for silicon, III-V, III-N, and graphene semiconductor devices and project future performance of plasma-wave THz devices.