The emission of waves is treated by solving the inhomogeneous wave equation and deriving an emission formula. The emission formula derived here may be used to describe the emission of waves in an arbitrary medium by an arbitrary source, described by an extraneous current. The current corresponding to electric and magnetic dipoles and electric quadrupoles is discussed in detail, and the electric dipole case is used to derive the Larmor formula, which describes emission by an accelerated nonrelativistic charge in vacuo. The more conventional treatment of emission based on the Lienard–Wierchert potentials is then developed. The back reaction of the radiating system to the emission of radiation may be taken into account in two different ways, depending on the context: by the use of quasi-linear theory, and through a radiation reaction force. These two procedures are discussed critically here.