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This talk concerns the application of dynamical systems techniques (specifically invariant anifold methods) and results from the classical three body problem as well as concatenated 3-body systems to the resonant transition and temporary capture of comets and to the design of space missions such as the {\it Genesis Discovery Mission} and missions to the moons of Jupiter. An exciting recent development is the observation that many comets and upcoming space missions make use of structures in the dynamics of the three body problem which dynamical systems researchers have, since the time of Poincar\'e, been investigating for their intrinsic interest. These structures involve heteroclinic and homoclinic connections between periodic orbits that enable new trajectory design of improved efficiency. The point of view developed is that the invariant manifold structures associated to the libration points as well as the associated heteroclinic connections are fundamental tools that can aid in understanding dynamical channels and transport throughout the solar system.