Magnetic skyrmions and other topologically protected nanostructures are investigated. Since skyrmions are mathematical rather than physical objects, they describe a wide variety of physical systems, from simple magnetic domain walls to complicated quantum phases with long-range many-body entanglement. Important distinctions concern the skyrmions’ relativistic character, their quantum-mechanical or classical nature, and the one- or many-body character of the wave functions. As specific examples we consider magnetic nanospirals, where the topology of a vortex-like spin state is protected by magnetostatic interactions, and edge currents in dilute magnetic semiconductors and metallic nanodots. Our analysis militates against giant orbital moments created by a mesocopically enhanced spin-orbit coupling.