This review outlines the present frontiers of magnet technology for accelerators, as driven by the demands of particle and nuclear physics, and surveys the grand challenges that are being faced by scientists and engineers developing superconducting, normal conducting and permanent magnets. At present, a strong driver for the development of superconducting magnet accelerator technology is without doubt the upgrade plan for the Large Hadron Collider at CERN. The demand for high field, large bore magnets for the LHC upgrade is, however, not the only challenge. A number of projects and proposals call for magnet R&D in a wide range of field, from the typical domain of permanent and electromagnets, up to few T, to very high field superconducting magnets in the range of tens of T, and bores, from minuscule few mm, to tens of cm, in dipole, quadrupole and solenoid configurations. The aim of this review is to present a summary of these challenges, to confront them to the state-of-the-art in magnet engineering, and finally to provide scope and motivation for targeted R&D in various domains of magnet technology.
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