The existence of a magnetic compass system allowing animals to maintain the direction of their migratory journeys was first shown in birds about fifty years ago. Over the past half century, a large amount of indirect, mainly behavioral, data on the features of the avian magnetic compass and its relationship with the perception of light has been obtained. Based on these data, the dominant idea suggests that the primary magnetoreceptor in birds is located in the retina, and the most popular hypothesis concerning operation of such a magnetoreceptor is the radical pair model. According to this model, the primary receptor molecules that perceive the magnetic field are cryptochromes expressed in the neurons of the avian retina. It is assumed that cryptochrome molecules localized in photoreceptor cells may have an ordered orientation relative to the retina plane. When photons are absorbed in the short wavelength range of the spectrum, cryptochromes would produce a chemical response depending on the direction of the external magnetic field. The sensitivity of photochemical reactions involving radical pairs in cryptochromes to a magnetic field is confirmed both by theoretical calculations and experimentally. However, up to date there is no experimental data obtained on the molecular mechanisms of further transduction of signal induced by a magnetic field. The existing hypotheses on possible nature of these mechanisms have some issues concerning their compatibility with the current concepts of the photoreception. These hypotheses ascribe special properties to the participants of the visual process both at the molecular and at the cellular level, which has not yet been proved experimentally. Thus, nowadays the science of magnetoreception is posed to consistently test the existing hypotheses on the molecular basis of avian magnetic compass.