Gender quotas have been adopted in more than one hundred countries around the world in recent years. While they are the subject of a growing literature, most existing work on these measures focuses on explaining their adoption and varied effects on the absolute numbers of women elected. Yet, quotas are often justified with reference to their anticipated effects on the representation of ‘women’s interests’ in the policy-making, as well as on democratic outcomes more generally. In this paper, we present some thoughts as to how scholars might undertake such research, in light of several complex dynamics: on-going debates on how to analyze women’s substantive representation, varied normative arguments with distinct expectations about links between the descriptive and substantive representation of women, and important differences in the design and conditions of adoption of individual quota policies. Based on these possibilities, we offer six sets of hypotheses as an initial step for undertaking individual and comparative case studies on the broader impact of gender quotas.