The United Kingdom will vote on June 23 in a yes-no referendum on whether to leave the European Union (Brexit). A case can be made for Brexit based on arguments about government, economics, law, and cultural identity. There are also many strong arguments for remaining in the EU, making this vote neither clear nor easy. This backgrounder fleshes out the full array of arguments for the Leave (pro-Brexit) and Remain (anti-Brexit) campaigns as each side views them from its own perspective. The paper concludes with a set of recommendations as to how the U.S. should view the debate in light of its own interests.