Parking functions are well-known objects in combinatorics. One interesting generalization of parking functions are parking completions. A parking completion corresponds to a set of preferences where all cars park assuming some of the spots on the street are already occupied. In this talk, we will explore how parking completions are related to restricted lattice paths. We will also present results for both the ordered and unordered variations of the problem by use of a pair of operations (termed Join and Split). A nice consequence of our results is a new volume formula for most Pitman-Stanley polytopes. This is joint work with H. Nam, P.E. Harris, G. Dorpalen-Barry, S. Butler, J.L. Martin, C. Hettle, and Q. Liang.