The goal is to describe how techniques from symplectic dynamics can be used to study orbit travel in three dimensions, for systems like the restricted 3-body problem from celestial mechanics. The pseudo-holomorphic curve theory initiated by Hofer, Wysocki and Zehnder gives a decomposition of the space into regions whose boundaries are surfaces transverse to the flow. (Pseudo-holomorphic curves are special minimal surfaces). One can label the regions A, B, C etc and form a directed graph. This gives us a natural language to discuss trajectories of orbits, a topic notorious for its complexity. Certain interesting features arise from this structure. I will describe how semi-local considerations lead to more global information and symbolic dynamics. This is joint work with Umberto Hryniewicz and Gerhard Knieper. The talk will address a general mathematical audience.