Despite significant advances in education and political participation, women remain underrepresented in leadership positions in politics and business across the globe. In many countries, policy-makers have responded by introducing gender quotas in politics and increasingly, many have expressed an interest in requiring gender quotas for corporate boards. This paper reviews the evidence on the equity and efficiency impacts of gender quotas for political positions and corporate board membership. Adoption of quotas by countries is likely correlated with attitudes about women within a country. However, the randomized allocation of political quotas in India and the unanticipated introduction of board quotas in Norway have allowed researchers to provide causal analysis and this review focuses on evidence from these two settings. The Indian evidence demonstrates that quotas increase female leadership and influences policy outcomes. In addition, rather than create a backlash against women, quotas can reduce gender discrimination in the long-term. The board quota evidence is more mixed. While female entry on boards is correlated with changing management practices, this change appears to adversely influence short-run profits. Whether this is partly driven by negative perceptions of female management choices remains an open question. Returning to the broader cross-country context, we find evidence in many different settings that political and corporate entities often act strategically to circumvent the intended impact of quotas. Consistent with this, we report suggestive evidence that the design of the quota and selection systems matter for increasing female leadership.