WWHeavily doped semiconductors, in particular Si:P and Si:B, have been prototype materials for the study of the metal–insulator (MI) transition at low temperature, T. Because of the statistical distribution of donors or acceptors in the (usually single–crystalline) host, disorder plays a crucial role for the MI transition. In addition, electron–electron interactions are important as evidenced by the rather large corrections to the Boltzmann conductivity already far above the MI transition. Usually, the MI transition is investigated by studying samples of varying dopant concentrations, N, although stress tuning and magnetic–field tuning have also been employed. An issue of considerable importance which we will discuss in this review is the critical behaviour of the electrical conductivity, σ(T→0)∼(N−Nc)μ, close to the critical dopant concentration Nc, i.e. the exponent puzzle of μ≈0.5 versus μ≈1. The question of critical behaviour of the Hall constant will also be addressed. We further discuss the role of magnetic moments on thermodynamic and transport properties close to the MI transition. It has been known for some time that localized moments which of course are present on the insulating side of the MI transition, exist also on the metallic side. Only recently, however, was their influence detected on a transport property, namely the thermoelectric power. We review some of the salient features of local magnetic moments at the MI transition and report on measurements of the specific heat and magnetization on the same samples. The direct comparison of thermodynamic quantities allows a test of models for local moments at the MI transition. Finally, thermoelectric–power measurements together with electrical resistivity reveal strong differences between uncompensated Si:P and compensated Si:(P,B) on the insulating side of the MI transition, with evidence of opening of a Hubbard gap in Si:P only considerably below Nc.