Basic relations relevant to the observation of radiative recombination are presented and experiments on both spontaneous and laser-stimulated recombination of ions with free electrons are reviewed. In particular, the observation of unexpected high spontaneous recombination rates at very low energies is discussed. The fundamental and applied interest in the observed rate enhancement effects has recently triggered new experimental and theoretical work which can provide new insight into the problem of direct recombination of antiprotons with positrons to form antihydrogen.