Magnetic Monopoles

Magnetic monopoles are hypothetical particles with magnetic charge. Their existence is predicted by string theory and grand unified theories, and if the temperature of the universe ever exceeded their mass, they should have been produced in large numbers. Yet, they have not been found in spite of extensive searches. I give a review of the theoretical and experimental status of magnetic monopoles, including the new MoEDAL experiment at the LHC. I also discuss theoretical problems in the calculation of their production rate in particle collisions.