The quantum theory of light in real media requires attention to a number of physical features. Even in near-transparent dielectrics, we have to incorporate dispersion, losses and the effects of interfaces. Here, we review the quantization of light in a dielectric and see how this affects radiative processes and light propagation. In the second half of the paper, we turn to optical forces and momentum. There we show why there are two rival force densities in a medium and also why there must be two distinct optical momenta. In the process, this resolves the century-old Abraham–Minkowski dilemma. This article is part of the theme issue ‘The quantum theory of light’.