One of the largest and most persistent features in the Alboran Sea is the Western Alboran Gyre (WAG), an anticyclonic recirculation bounded by the Atlantic Jet (AJ) to the north and the Moroccan coast to the south. Eulerian budgets from several months of a high-resolution model run are used to examine the exchange of water across the Eulerian WAG’s boundary and the processes affecting the salinity, temperature, and vorticity of the WAG. The volume transport across the sides of the WAG is found to be related to vertical isopycnal movement at the base of the gyre. Advection is found to drive a decay in the salinity minimum and anticyclonic vorticity of the Eulerian WAG. Given the large contributions of advection, a Lagrangian analysis is performed, revealing geometric aspects of the exchange that are hidden in an Eulerian view. In particular, stable and unstable manifolds identify a stirring region around the outer reaches of the gyre where water is exchanged with the WAG on a timescale of weeks. Its complement is an inner core that expands with depth and exchanges water with its surroundings on much longer timescales. The 3D evolution of one parcel, or lobe, of water as it enters the WAG is also described, identifying a general Lagrangian subduction pathway.