The magnet design of the new ITER-FEAT machine comprises 18 toroidal field (TF) coils, a central solenoid (CS), 6 poloidal field coils and correction coils. A key driver of this new design is the requirement to generate and control plasmas with a relatively high elongation (κ95 = 1.7) and a relatively high triangularity (δ95 = 0.35). This has led to a design where the CS is vertically segmented and self-standing and the TF coils are wedged along their inboard legs. Another important design driver is the requirement to achieve a high operational reliability of the magnets, and this has resulted in several unconventional designs, and in particular the use of conductors supported in radial plates for the winding pack of the TF coils. A key mechanical issue is the cyclic loading of the TF coil cases due to the out-of-plane loads which result from the interaction of the TF coil current and the poloidal field. These loads are resisted by a combination of shear keys and `pre-compression' rings able to provide a centripetal preload at assembly. The fatigue life of the CS conductor jacket is another issue, as it determines the CS performance in terms of the flux generation. Two jacket materials and designs are under study. Since 1993, the ITER magnet R&D programme has been focused on the manufacture and testing of a CS and a TF model coil. During its testing, the CS model coil has successfully achieved all its performance targets in DC and AC operations. The manufacture of the TF model coil is complete. The manufacture of segments of the full scale TF coil case is another important and successful part of this programme and is near completion. New R&D effort is now being initiated to cover specific aspects of the ITER-FEAT design.