We discuss the biological effects of weak magnetic fields, a problem that has gone unresolved for nearly half a century. We consider the spin—chemical mechanism of radical pairs, which is prevalent in the literature aiming to explain the observed phenomena. The effectiveness of this mechanism is limited by spin relaxation. The relaxation rate is estimated for a radical in a protein via the Zeeman, hyperfine, spin—orbit, and exchange interactions. Taking the relaxation and chemical kinetics into account, we present an analytic solution of the Liouville—von Neumann equation for two electrons and a nucleus, which relates the magnitude of the effects to the relaxation rate. Various aspects of the solution are discussed: the influence of the radiofrequency and hypomagnetic fields, the role of quantum entanglement, theoretical challenges and prospects, and others.