Future space telescopes will require more demanding requirements—such as bigger primary mirrors for higher resolution images and complex, cryo-cooled telescope designs for infrared imaging in space. To achieve these science goals, however, spacecraft science mission costs must be minimized. These include set mission times and fuel capacity which limit the amount, type, and timing of maneuvers that can be achieved. This dissertation studies both fuel and time optimal orbital techniques for (1) the delivery of space telescopes to their final orbit and (2) efficient maneuvers during space telescope observations. The first part introduces a mission concept for a segmented space telescope assembled with modular spacecraft carrying individual mirror segments. They are propelled by solar sails towards Sun-Earth L2 and then transferred onto a Lissajous orbit for assembly. I present optimal orbital procedures for computing the full trajectory design and optimal scheduling of launches to assemble the full primary mirror in a period of 11 years. The second part studies the operation of starlight suppression via starshades—an external occulter spacecraft that flies in formation with a space telescope along the line of sight to a target star and enables exoplanet direct imaging. I present analytical models for the formation flying kinematics and simulate maneuvers to remain within strict tolerances of that formation. I then present metrics and techniques for scheduling optimal observations for specific target lists that both save fuel costs and increase science output. I also study the retargeting problem: once the starshade and telescope finish an observation, the starshade must align itself with a new star. I present ways of exploring the vast search space of retargeting trajectories and apply them to the optimal scheduling of exoplanet direct imaging mission simulations.