Observing astrophysical magnetic fields is difficult. Nonetheless, fields of surprisingly consistent amplitudes on the order of microgauss have been discovered in many galaxies and clusters of galaxies. So far, the generation of these fields has remained a mystery. For a long time, scientists tried to conceive of a mechanism by which tiny primordial fields would be created in the early universe. Later, during gravitational collapse, such fields could be amplified--for example, by means of a dynamo mechanism--and thereby lead to the observed fields in galaxies and clusters. [...]