Globular clusters are traditionally pictured as simple stellar populations in terms of their structure, kinematics, and abundances. However, many recent and upcoming observational studies are challenging this picture. In particular, observations continually show the presence of differential rotation and velocity dispersion anisotropy which are key kinematical fingerprints tied to the cluster’s dynamical history. These observational results have motivated our effort to characterize the evolution of the internal kinematics of globular clusters via N-body simulations. I will present some of the new results from simulations that show unexpected complexities in the kinematics, such as clusters being unable to maintain or attain full tidal synchronization, complex rotation axis orientations, different kinematical signatures for multiple stellar populations in a cluster, and anisotropic mass segregation.