Three topics are discussed in the dissertation. The first topic addresses new ways of parameterizing the optimal control variables when maximizing the final spacecraft mass of low-thrust, gravity-assist trajectories. When the thrust is parameterized by on/off times (i.e. maximum thrust/coast arcs) and the steering angles are parameterized via Chebyshev series, the computational time can be reduced by an order of magnitude. The second topic is to design trajectories to the outer planets for a spacecraft using nuclear electric propulsion. Dozens of low-thrust, gravity-assist, rendezvous trajectories to Jupiter, Saturn, Uranus, Neptune, and Pluto are found. A rendezvous with Pluto via gravity assists with Earth and Jupiter requires a flight time of only 10 years for a propellant mass fraction of 50%. The final topic considers various end-of-life options for the Cassini mission, such as crashing the spacecraft into Saturn's atmosphere. A Tisserand surface technique is developed that aids the design of gravity-assist trajectories that impact Saturn. Another encore scenario considers using gravity assists from Saturn's largest moon, Titan, to eject Cassini from the Saturnian system to reach other gas giants.