The magnetic response of most natural materials, characterized by magnetic permeability, is generally weak. Particularly, in the optical range, the weakness of magnetic effects is directly related to the asymmetry between electric and magnetic charges. Harnessing artificial magnetism started with a pursuit of metamaterial design exhibiting magnetic properties. The first demonstration of artificial magnetism was given by a plasmonic nanostructure called split-ring resonators. Engineered circulating currents form magnetic plasmons, acting as the source of artificial magnetism in response to external electromagnetic excitation. In the past two decades, magnetic plasmons supported by plasmonic nanostructures have become an active topic of study. This Perspective reviews the latest studies on magnetic plasmons in plasmonic nanostructures. A comprehensive summary of various plasmonic nanostructures supporting magnetic plasmons, including split-ring resonators, metal–insulator–metal structures, metallic deep groove arrays, and plasmonic nanoclusters, is presented. Fundamental studies and applications based on magnetic plasmons are discussed. The formidable challenges and the prospects of the future study directions on developing magnetic plasmonic nanostructures are proposed.