Magnetic materials have become controllable on the nanometre scale. Such fine structures exhibit a wide range of fascinating phenomena, such as lowdimensional magnetism, induced magnetization in noble metals, electron interference patterns, oscillatory magnetic coupling and 'giant' magnetoresistance. Magnetic multilayers with nanometre spacings are among the first metallic quantum structures to become incorporated into electronic devices, such as reading heads for hard discs. This article is intended to familiarize the reader with the physics and technology of magnetic nanostructures. It starts out with recent progress in nanofabrication, gives a tutorial on the connection between electronic states and magnetic properties, surveys the state of the art in characterization techniques, explains unique phenomena in two-, one- and zero-dimensional structures, points out applications in magnetic storage technology and considers fundamental limits to storage density. Particular emphasis is placed on the connection between magnetism and the underlying electronic states, such as the spin-split energy bands, s, p versus d states, surface states, and quantum well states.