Migrating birds fly thousand miles without having a map, or a GPS unit.But they may carry their own sensitive navigational tool, which allows them "see" the Earth's magnetic field. Here we review the important physical and chemical constraints on a possible compass sensor and discuss the suggestion that radical pairs in a photoreceptor cryptochrome might provide a biological realization for a magnetic compass. Finally, we review the current evidence supporting a role for radical pair reactions in the magnetic compass of birds.