We consider the economics and the design of border adjustments (BAs) under a carbon tax. BAs are taxes on imports and rebates on exports on the emissions from the production of a good. They are thought to be a method of reducing inefficiencies from a unilateral carbon price, such as shifts in the location of production, known as leakage. After examining the basic economics of BAs, we examine three design issues: which goods BAs should apply to, which emissions from the production of those goods should be taxed, and from and to which countries BAs should apply. We conclude that BAs will impose high administrative costs and need strong welfare justifications.