Microwave current oscillations in n-type polar semiconductors at high electric fields were first observed by Gunn in 1963. T h e basic physical mechanism responsible for the effect is the progressive transfer of hot electrons from high mobility valleys to low mobility valleys in the conduction-band structure as the field increases. The resulting negative differential mobility makes the homogeneous electron distribution unstable. Narrow domains of extremely high field build up 97 98 P. N . Butcher which propagate uniformly through the specimen. Recent theoretical and experimental studies of the electron-transfer mechanism and domain propagation are described. T h e emphasis is on the basic phenomena in gallium arsenide and microwave applications of the effect are not discussed.