Galaxy Mergers through Cosmic Time Galaxies grow with time through both discrete galaxy mergers and smooth gas accretion. When and how this growth occurs, and the role of mergers in defining the properties of today's galaxies, remain outstanding observational questions. Observational estimates of the galaxy merger rate and its evolution can vary by factors of 10, depending upon the method and assumptions used to count mergers. Using physical-motivated timescales from a large suite of galaxy merger simulations, I am able to reconcile the discrepancies between different measurements of the galaxy merger rate at z<1. The frequency of gas-rich mergers has increased strongly from z~0 to z~1, while the global galaxy merger rate evolved more modestly. Finally, I will discuss the prospects for identifying galaxy mergers at z~2 and beyond with the Cosmic Assembly Near-infrared Extragalactic Legacy Survey.