Even though resilience and sustainability are the two overarching strategic goals of contemporary supply chain management, very few studies have investigated the relationship between resilience and sustainability practices. To increase our theoretical understanding of this important relationship, this paper examines the extent to which supply chain managers perceive tensions and complementarities between both sets of practices. Using a paradox theory lens, the paper conducted in‐depth interviews with 31 supply chain managers in Western Europe and the Middle East that reveal a complex and multifaceted relationship. Namely, our findings indicate that some supply chain managers perceive the relationship as conflictive, others as synergistic, whereas a third group sees them as fundamentally orthogonal to each other. Furthermore, our findings uncover specific perceived complementarities and tension areas. Taken together, in responding to calls for research on the topic, our findings contribute to the advancement of theory regarding supply chain resilience and supply chain sustainability practices and address the need to shed more light on the tensions faced by supply chain managers when implementing distinct sets of supply chain practices.