In a world where knowledge accumulates faster than individuals' capacity to master it, storing a society's body of knowledge requires distributing it across an expanding variety of experts, and using it involves creating networks of individuals with complementary skills. We use Swedish educational and employment data to construct networks that help quantify educational complementarity. Based on these networks, we find that wages are higher when workers work with complementary coworkers. Moreover, the networks not only help understand workers' wages, but also their career moves, the distribution of college wage premiums, and the well-known fact that wages tend to be higher in larger firms and cities.