Migratory birds travel vast distances each year, finding their way by various means, including a remarkable ability to perceive the Earth's magnetic field. Although it has been known for 40 years that birds possess a magnetic compass, avian magnetoreception is poorly understood at all levels from the primary biophysical detection events, signal transduction pathways and neurophysiology, to the processing of information in the brain. It has been proposed that the primary detector is a specialized ocular photoreceptor that plays host to magnetically sensitive photochemical reactions having radical pairs as fleeting intermediates. Here, we present a physical chemist's perspective on the "radical pair mechanism" of compass magnetoreception in birds. We outline the essential chemical requirements for detecting the direction of an Earth-strength ≈50 μT magnetic field and comment on the likelihood that these might be satisfied in a biologically plausible receptor. Our survey concludes with a discussion of cryptochrome, the photoactive protein that has been put forward as the magnetoreceptor molecule.