Radio continuum emission due to thermal bremsstrahlung and optical Hα spectral line emission arise from processes involving similar atomic entities and physical conditions. The relationship between the flux density of the emission from the two processes is mainly a function of the electron temperature of the emitting region, modified by other factors such as the mode of radiation transfer in the hydrogen spectrum. On the other hand, radio continuum radiation due to non-thermal synchrotron emission is formed by species and processes not involved in thermal emission. As a consequence, differences between the observed radio continuum emission and Hα emission from cosmic sources can provide reliable information on a variety of important physical aspects of the sources, including the relative importance of thermal and non-thermal radio emission and the degree of optical obscuration. This paper reviews the theory of the formation of Hα and the radio continuum in the interstellar medium (ISM), discusses some of the factors that must be considered in comparing observations made in the two frequency regimes, and summarises the properties of some classes of galactic object that emit both optical and radio radiation.