The existence of the magnetic compass system was first shown in birds. Since then, a large amount of data has been accumulated on the performance of the avian magnetic compass and its relationship with visual reception. The current dominant concept is that the receptor for the magnetic compass in birds is located in the retina. The most popular hypothesis for the mechanism of operation of magnetic field receptors is the radical pair model, and a candidate for the role of the primary magnetoreceptor molecule is cryptochrome, and more specifically, its isoform, cryptochrome 4a. In recent years, data have been published on the interaction of cryptochrome with some proteins involved in the phototransduction cascade, as well as promising data from electrophysiological studies combining light and magnetic stimuli. In addition, a number of morphological studies of the avian retina also allow us to narrow down the range of promising cells for the role of a magnetoreceptor, and the double cone is currently the most likely candidate. In this review, we discuss the latest research data in this area.