  In this review, we discuss recent developments in both the theory and the
experimental searches of magnetic monopoles in past, current and future
colliders and in the Cosmos. The theoretical models include, apart from the
standard Grand Unified Theories, extensions of the Standard Model that admit
magnetic monopole solutions with finite energy and masses that can be as light
as a few TeV. Specifically, we discuss, among other scenarios, modified
Cho-Maison monopoles and magnetic monopoles in (string-inspired, higher
derivative) Born-Infeld extensions of the hypercharge sector of the Standard
Model. We also outline the conditions for which effective field theories
describing the interaction of monopoles with photons are valid and can be used
for result interpretation in monopole production at colliders. The experimental
part of the review focuses on, past and present, cosmic and collider searches,
including the latest bounds on monopole masses and magnetic charges by the
ATLAS and MoEDAL experiments at the LHC, as well as prospects for future
searches.
