This article reviews three strands in the scholarship on the populist radical right (PRR). It covers both political parties and extra-parliamentary mobilization in contemporary European democracies. After definitional issues and case selection, the authors first discuss demand-side approaches to the fortunes of the PRR. Subsequently, supply-side approaches are assessed, namely political opportunity explanations and internal supply-side factors, referring to leadership, organization and ideological positioning. Third, research on the consequences of the emergence and rise of these parties and movements is examined: do they constitute a corrective or a threat to democracy? The authors discuss the growing literature on the impact on established parties' policies, the policies themselves, and citizens' behaviour. The review concludes with future directions for theorizing and research.