Abstract
Searches for magnetic monopoles ([Formula: see text]s) are a fascinating interdisciplinary area with implications for fundamental theories, particle physics, astrophysics, and cosmology. The quantum theory of [Formula: see text]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. [Formula: see text]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 [Formula: see text]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 [Formula: see text]s at accelerators for GUTs, superheavy [Formula: see text]s in the penetrating cosmic radiation, and intermediate-mass [Formula: see text]s at high altitudes, emphasizing the most recent results and future perspectives.
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