Design of matching systems between refugees and states or local areas is emerging as one of the most promising solutions to problems in refugee resettlement. We describe the basics of two-sided matching theory used in a number of allocation problems, such as school choice, where both sides need to agree to the match. We then explain how these insights can be applied to international refugee matching in the context of the European Union and examine how refugee matching might work within the United Kingdom, Canada, and the United States. Public attention and activism often focuses on the question of "how many?" In the context of incredibly limited supply of resettlement spaces, this is not unreasonable. The proportion of refugees in situations of "protracted displacement" (where more than 25,000 refugees have been in exile for more than five years) was estimated at two-thirds in 2009 (Loescher, Gil, and Milner 2009), prior to the current Syrian crisis. For refugees in protracted situations, the average length of stay is 17 years. There are now some 21.3 million refugees in the world, out of some 65.3 million forcibly displaced worldwide (UNHCR 2016a). In this context, global resettlement capacity is awesomely, ludicrously inadequate: in 2015, states admitted 107,100 refugees for resettlement, of which the United States accepted more than half (66,500) (UNHCR 2016b, 3). As one recent group of refugee experts uncompromisingly put it, "the current global system for refugee protection is broken" (Dauvergne and Hathaway 2016). However, as with any scarce resource, it is also vital to consider how the limited resettlement capacity of the states can be used most effectively. In this paper, we focus on the question that arises after it has been decided that a given group of refugees will be resettled. Instead