A doped semiconductor can be viewed as a mixed electronic-ionic conductor, with the dopants as mobile ions. Normally the temperature range where this becomes true is not even close to that where the (opto)electronic properties of the material are of interest. However, notable exceptions exist and these are reviewed here, with special emphasis on those cases where semiconductivity is preserved when the (mobile) dopant concentration changes and ambipolar behavior can be obtained by dopant mobility. Dopant diffusion and drift are of interest not only in materials such as Si:Li, known from its use in radiation detectors, but also in other semiconductors, ranging from II-VIs and related compounds, such as (Hg,Cd)Te and CuInSe2 to III-Vs and potential high temperature semiconductors, such as diamond. Better understanding of the phenomena is important also because of the implications that it has for device miniaturization, as dopant diffusion and drift put chemical limits to device stability. Such understanding can also make dopant electromigration useful for low-temperature doping. Some basic theory for electric-field-induced dopant migration is given and compared to experiments.