The Compact Torus Accelerator (CTA), under development at Lawrence Livermore National Laboratory, offers the promise of a low-cost, high-efficiency, high-energy, high-power-density driver for ICF and MICF (Magnetically Insulated ICF) type fusion systems. A CTA with 100 MJ driver capacitor bank energy is predicted to deliver ~30 MJ CT kinetic energy to a 1 cm2 target in several nanoseconds for a power density of ~1016 watts/cm2. The estimated cost of delivered energy is ~3$/Joule. We discuss indirect-drive ICF with a DT fusion energy gain Q = 70 for a total yield of 2 GJ. A reactor system for CT injection, target emplacement, containment, energy recovery, and breeding will be described. The CTA naturally lends itself as a driver for MICF where an energetic (≈100 MJ) CT is injected into a containment sphere generating shock heating which initiates a magnetically insulated DT burn with refueling for Q ≃ 70 and a fusion yield of 7 GJ. The containment sphere, which is chosen to be several 14 MeV neutron mfp's thick, is vaporized and heated by fusion neutrons and expands into the main reactor containment chamber to form the working gas for direct electrical energy recovery through an MHD generator cycle. Application of the MICF system to spaceship propulsion will also be discussed.