Fusion magnet technology has made spectacular advances in the past decade; to wit, the Mirror Fusion Test Facility and the Large Coil Project. However, further advances are still required for advanced economical fusion reactors. Higher fields to 14 T and radiation-hardened superconductors and insulators will be necessary. Coupled with high rates of nuclear heating and pulsed losses, the next-generation magnets will need still higher current density, better stability and quench protection. Cable-in-conduit conductors coupled with polyimide insulations and better steels seem-to be the appropriate path. Neutron fluenoes up to 10 neutrons/cm in niobium tin are achievable. In the future, other amorphous superconductors could raise these limits further to extend reactor life or decrease the neutron shielding and corresponding reactor size.