Magnetic Monopoles at the LHC and in the Cosmos

Dirac showed in 1931 that the existence of one magnetic monopole in the Universe would explain why electric charge is quantised. The monopole also arises as a natural consequence of Grand Unification theories. While colliders provide direct laboratory studies, long-lived particles with masses beyond the reach of man-made accelerators would have been produced in the early Universe and still be present today. I shall review experimental searches for highly-ionising particles at colliders, focusing on recent developments at the LHC. I shall also review searches for monopoles with cosmic-ray detectors and trapped in matter, and propose a few promising avenues for the future.