Periodic orbits, quasiperiodic orbits, and invariant manifolds are key to obtaining an overall understanding of motion and transport within celestial mechanics models.  These topics will be introduced primarily in the circular restricted three-body problem with other examples in more complex models including the real-world ephemeris.  Design consideration for trajectories using these components and heteroclinic connections for astrodynamics applications will also be introduced.  Particular applications to the design of trajectories traveling to the moon and Jovian tours will be presented as well.