We study optimal nonlinear taxation of single and married households. Taxes on couples depend on the earnings of both spouses and are an example of multi-dimensional tax schedules. We develop novel analytical techniques to study properties of such taxes. We show that the optimal marginal taxes for married individuals are generally lower than for single individuals because resource-sharing within couples provides socially valuable redistribution. Under realistic assumptions, the optimal tax rates for married individuals increase with the correlation of spousal earnings, the marginal tax rates for one spouse increase (decrease) in the earnings of the other if both spouses have low (high) earnings, and the primary earner faces lower marginal taxes than the secondary earner. We extend our approach to consider normative tax implications of within-family public goods, home production, extensive margin in labor supply, selection into marriage, bargaining over marital surplus, and gender differences.