Dimensional reduction of Yang-Mills theory gives rise to the Yang-Mills-Higgs functional in 3 dimensions, with special critical points known as "magnetic monopoles" analogous to instantons. This talk will give an overview of these objects, their soliton properties, and their associated moduli spaces, which constitute complete, smooth hyper-Kahler manifolds indexed by a topologically quantized "magnetic charge". I will also give a brief sketch of the several remarkably equivalent formulations of monopoles, including Nahm's equations, spectral curves in the twistor space, and rational maps of the Riemann sphere, along with open questions and areas of current research.