The basic principles of IMPATT diodes as microwave devices are reviewed and the current status of these devices concerning power output and efficiency is given. The main purpose of this paper, however, is to discuss the nonlinear properties of these diodes which are useful in the design of amplifiers, oscillators, and other microwave devices. The main results of this paper are obtained from a digital computer analysis where an approximate, but realistic, diode model is employed. A detailed comparison of complementary silicon diodes as well as GaAs diodes concerning power output and efficiency is given. The effects of doping profile, current density, temperature, and material parameters on the performance of these devices have been investigated and are summarized. Saturation effects which limit the efficiency and power output of these devices are described and optimum efficiencies which can be achieved for various doping profiles are given. A comparison between single-sided and double-drift diodes in both silicon and GaAs is also presented.