We review basic results of quantum electrodynamics for the relaxation of a two-level systems coupled to the radiation field in a photonic structure. In the weak coupling regime, the spontaneous emission rate is proportional to the local mode density. This quantity can be obtained by solving classical Maxwell equations, and for that purpose numerical simulation schemes both in the frequency and time domains are described. Our examples focus on model structures in two and three dimensions. A tutorial overview of quantum electrodynamics calculations close to a photonic band edge is given, with emphasis on non-exponential spontaneous decay.