Wages for the vast majority of workers have stagnated in the United States since the 1980s. We offer two coexisting explanations based on rising market power: 1. Monopsony, where dominant firms exploit the limited mobility of their own workers to pay lower wages; and 2. Monopoly, where dominant firms charge too high prices for what they sell, which lowers production and the demand for labor, and hence wages economy-wide. Using U.S. Census data for the period 1997-2016, we estimate that 60 percent of wage stagnation is due to the rise of monopoly, and that share is growing. The remainder is due to monopsony.