Status of Searches for Magnetic Monopoles

Searches for magnetic monopoles (s) are a fascinating interdisciplinary area with implications for fundamental theories, particle physics, astrophysics, and cosmology. The quantum theory of s, and its consistency with electrodynamics, was originally derived by Dirac, marking the beginning of the search for classical monopoles at every new accelerator, including the Large Hadron Collider. s are required by Grand Unification Theories (GUTs), but unlike classical monopoles they would be incredibly massive, out of reach for any conceivable accelerator. Significant effort has been made to search for s in the cosmic radiation as relic particles from the early Universe in the widest experimentally available range of mass and velocity. In this review, we discuss the status of the searches for classical s at accelerators for GUTs, superheavy s in the penetrating cosmic radiation, and intermediate-mass s at high altitudes, emphasizing the most recent results and future perspectives.