Plasma thrusters are challenging the monopoly of chemical thrusters in space propulsion. The specific energy that can be deposited into a plasma beam is orders of magnitude larger than the specific chemical energy of known fuels. Plasma thrusters constitute a vast family of devices ranging from already commercial thrusters to incipient laboratory prototypes. Figures of merit in plasma propulsion are discussed. Plasma processes and conditions differ widely from one thruster to another, with the pre-eminence of magnetized, weakly collisional plasmas. Energy is imparted to the plasma via either energetic electron injection, biased electrodes or electromagnetic irradiation. Plasma acceleration can be electrothermal, electrostatic or electromagnetic. Plasma-wall interaction affects energy deposition and erosion of thruster elements, and thus is central for thruster efficiency and lifetime. Magnetic confinement and magnetic nozzles are present in several devices. Oscillations and turbulent transport are intrinsic to the performances of some thrusters. Several thrusters are selected in order to discuss these relevant plasma phenomena.