This article provides an introduction to science advisory structures in elected legislatures; an arena of public decision-making which, although critical to the healthy functioning of democratic societies, has been largely neglected in recent discussions of science advice. The article begins by contrasting the functions and operating environments of legislatures with those of executive branches of governments, examining how these differences shape the requirements of their respective science advisory structures. A study of three national legislative science advice units within Europe is then presented, revealing a range of advisory structures and practices. These variations in approach suggest different underpinning conceptions about both why science advice is being provided, and how science advice can most effectively influence a legislature's activities. Given these differences, and our currently limited comparative understanding of the influence of scientific knowledge across different spheres of public decision-making, we argue that more attention needs to be focused on the difficult challenge of mapping and understanding legislative science advisory structures via a comparative international study. We close by arguing that an international comparative exercise of this type could significantly improve our understanding of the different influences science advisory practices and structures can have on the function of our democratic societies' deliberative bodies. This article is published as part of a collection on scientific advice to governments.