Recent research at the University of Colorado (CU) have implemented robust computational algorithms for precisely finding and continuing quasi-periodic orbits of dimension 2 and higher, along with their manifolds (Z. Olikara, PhD. Thesis, 2016). The use of these higher-dimensional orbits can have significant impacts on the design of heteroclinic transfers, along with many other applications. This arises due to the relatively high phase space co-dimensions of the stable and unstable manifolds of these orbits, making it is easier to find connections between different quasi-periodic tori of the same energy. Similarly, the ability to compute these higher-dimensional tori also enables the robust continuation of periodic orbits and tori in periodically perturbed problems, such as the elliptic-restricted 3-body problem or the problem of orbiting about an asteroid in a complex rotation state. There are also significant applications to orbit mechanics in complex environments and formation flight of satellites. This talk will describe our recent, current and future research on these problems.