Possible mechanisms for producing the observed broad radio spectra of compact extragalactic radio sources are discussed. The explanations considered are: (a) superposition of the spectra of sub-components, (b) inhomogeneous synchrotron sources, and (c) synchrotron radiation from “non-standard” energetic electron spectra. These three models have been compared with results of spectral and VLBI observations. These comparisons indicate: (1) if the “superposition” hypothesis is correct, then the subcomponents themselves must be inhomogeneous synchrotron sources, (2) there is apparently no general inhomogeneous synchrotron source which characterizes compact extra-galactic sources, and (3) many compact sources have spectra which resemble synchrotron radiation from a relativistic Maxwellian electron spectrum, but the inferred electron energies and magnetic fields have a wide range of values. VLBI observations of a selected sample of sources generally favor a single component model, but cannot distinguish between models (b) and (c).