Globular clusters are found in the halos of all types of galaxies, and have been shown to play major roles in the formation of stars and galaxies. The purpose of this thesis is to advance our level of understanding of the dynamical evolution of globular clusters through N-body simulations of clusters with a range of circular, eccentric, and inclined orbits. Theoretical studies have historically assumed that globular clusters experience a static tidal field, however the orbits of globular clusters are all non-circular and the tidal field of most galaxies is not symmetric. Understanding how clusters evolve in realistic potentials allows for them to be used to constrain the formation, merger history, and evolution of a host galaxy and even map out the current size, shape, and strength of a galaxy's gravitational field. We find that dense and compact clusters evolve as if they are in isolation, despite being subject to a non-static tidal field. For larger clusters, tidal shocks and heating inject energy into the cluster and significantly alter its evolution compared to previous studies. We describe how a non-static field alters the mass loss rate and relaxation time of a cluster, and propose methods for calculating a cluster's size and orbit. We then apply our work to clusters in the giant galaxies M87, NGC 1399, and NGC 5128. We consider each cluster population to be a collection of metal poor and metal rich clusters and generate models with a range of orbital distributions. From our models we constrain the orbital anisotropy profile of each galaxy, place constraints on their formation and merger histories, and explore the effects of nearby galaxies on cluster evolution. By advancing studies of globular cluster evolution to include the effects of a non-static tidal field, we have made an important step towards accurately modelling globular clusters from birth to dissolution. Our work opens the door for globular clusters to be used as tools to study galaxy formation, evolution, and structure. Future studies will explore how galaxy formation and growth via the hierarchical merger of smaller galaxies will affect cluster evolution. / Thesis / Doctor of Philosophy (PhD)