A rigorous theory of radiation from dipoles embedded inside an arbitrary multilayer system is presented. In particular, we derive explicit expressions for the angular distribution of the electromagnetic field and the intensity radiated by the dipole into the surrounding media. Under the assumptions of mutual incoherence of the dipole radiation the calculations are extended to a layer of radiating dipoles. Special configurations corresponding to (i) a single dipole near a dielectric interface, (ii) a dipole layer surrounded by semi-infinite dielectric media, and (iii) a dipole layer placed on top of a waveguide layer are discussed in detail. This theoretical analysis has important consequences for the optimization of optical chemical sensors and biosensors that are based on fluorescence emission.