Since the beginning of the Russian invasion of Ukraine one week ago, hundreds of thousands of Ukrainians have fled the country. The United Nations High Commissioner for Refugees (UNHCR) estimated that 660,000 Ukrainians had crossed into neighboring countries as of March 1, 2021, with the majority arriving in Poland as well as Hungary, Moldova, Romania, Slovakia and other European states. These numbers are in addition to at least 160,000 Ukrainians who have been internally displaced in the last week. Whether the number of refugees and internally displaced Ukrainians continues to climb depends on the nature of the conflict; if fighting continues and if Russia solidifies its occupation over large parts of the country, we can expect the number of both these groups to rise. This issue brief examines European and potential U.S. responses to the growing crisis.