What are the optimal tariffs of the US? What tariffs would prevail in a worldwide trade war? How costly would be a breakdown of international trade policy cooperation? And what is the scope for future multilateral trade negotiations? I address these and other questions using a unified framework which nests traditional, new trade, and political economy motives for protection. I find that US optimal tariffs average 60 percent, world trade war tariffs average 58 percent, the welfare losses from a breakdown of international trade policy cooperation average 3.5 percent, and the possible welfare gains from future multilateral trade negotiations average 0.3 percent.