Union membership in U.S. displayed a ∩-shaped pattern over the 20th century, while income inequality sketched a ∪. A model of unions is developed to analyze this phenomenon. There is a distribution of productivity across ﬁrms in the economy. Firms hire capital, plus skilled and unskilled labor. Unionization is a costly process. A union chooses how many ﬁrms to organize and the union wage. Simulation of the model establishes that skill-biased technological change, which affects the productivity of skilled labor relative to unskilled labor, can potentially explain the above facts. Statistical analysis suggests that skill-biased technological change is an important factor in deunionization.