Tens of thousands of refugees are permanently resettled from refugee camps to hosting countries every year. In the past, placement of refugees was essentially ad hoc, but more recently resettlement agencies have been trying to place refugees systematically in order to improve their outcomes. Yet, even at present, refugee resettlement processes account for neither the priorities of hosting communities nor the preferences of refugees themselves. Building on models from two-sided matching theory, we introduce a new framework for matching with multidimensional constraints that models refugee families’ needs for multiple units of different services, as well as the service capacities of localities. We propose four refugee resettlement mechanisms and two solution concepts that can be used in refugee resettlement matching under various institutional and informational constraints. Our mechanisms can improve match efficiency, respect priorities of localities, and incentivize refugees to report where they would prefer to settle.