Hierarchical models of galaxy formation predict that galaxy mergers represent a significant transitional stage of rapid supermassive black hole (SMBH) growth. Yet, the connection between the merging process and enhanced active galactic nuclei (AGN) activity as well as the timescale of SMBH mergers remains highly uncertain. The breakthrough in reconciling the importance of galaxy mergers with black hole growth lies in a thoroughly-studied census of dual AGN across cosmic history, which will be enabled by next-generation observational capabilities, theoretical advances, and simulations. This white paper outlines the key questions in galaxy mergers, dual and offset AGN, and proposes multiwavelength solutions using future high-resolution observatories in the X-rays (AXIS, Lynx), near and mid-infrared (30 meter class telescopes, JWST), and submillimeter (ALMA).