While case studies and theoretical approaches which analyze the spread of international norms and their impact on policy formation are prevalent in international relations theory and international law, the contributions to this special issue attempt to take this literature further by critically reviewing the relation between norm implementation and norm acceptance. To that end, we have asked a range of authors to examine cases in which prominent fundamental norms are contested. Instead of identifying these cases as indicators for the absence or decrease in the relevance of norms for international relations, these articles recommend refining research on norm application in order to account for such observations with better theory. In this introduction, the main research assumptions and approach of the critical constructivist perspective are reviewed, followed by an overview of the case studies assembled in this special issue and how they provide examples of an extended research agenda in the field of international norms with regard to different policy areas and fields of international cooperation and conflict. Finally, we offer a summary of what this special issue contributes to research on norms in current international relations.