Advances in fusion energy research now allow the construction of Q = 1 Tokamaks and make possible a new type of nuclear energy reactor: the Fusion-Fission Hybrid. The Hybrid makes advantageous the fact that the easiest fusion reaction : DT fusion, produces a 14MeV neutron which can drive much more energetic fission reactions in a fissile blanket. This solves many problems seen in pure fusion and allows light-water fission reactor technology for power reactors with fusion cores. Two basic types of Hybrid reactors are possible. One type, a waste treatment reactor, uses a Q ~ 1 fusion core to transmute high-level waste into shorter-lived isotopes for more convenient disposal, thus solving the concerns related to long lived radioactive byproducts and long term nuclear waste. The second type, the Fusion Controlled Fission Reactor uses a fusion core to excite and control fission chain reactions in a fission blanket for power production. Here the fusion reactor is Q << 1 since it only needs to supply enough neutrons to bring the fission blanket to criticality. Assuming the delayed neutron fraction in a fission reactor is required for a fusion reactor to create criticality indicates a density-confinement time or nï´E =1.5 × 1010 for ÂHybrid BreakevenÂ or 1/10,000 of Lawson Criterion. Such a hybrid reactor can provide space nuclear power based on Thorium transmutation to U-233 in space by using a fusion neutron source.