This paper studies how directors' reputational concerns affect board structure, corporate governance, and firm value. In our setting, directors affect their firms' governance, and governance in turn affects firms' demand for new directors. Whether the labor market rewards a shareholder-friendly or management-friendly reputation is determined in equilibrium and depends on aggregate governance. We show that directors' desire to be invited to other boards creates strategic complementarity of corporate governance across firms. Directors' reputational concerns amplify the governance system: strong systems become stronger and weak systems become weaker. We derive implications for multiple directorships, board size, transparency, and board independence.