The heavy fermion semiconductors, or Kondo insulators, are very narrow gap
semiconductors in which the properties show unusual temperature dependencie
s. We shall review their properties and show how they can be interpreted in
terms of an electronic band structure, with a temperature dependent hybrid
ization gap together with temperature dependent quasi-particle lifetimes. T
he properties of these semiconductors are very sensitive to impurities, whi
ch can enhance the incipient antiferromagnetic correlations and precipitate
a magnetic instability.