As humanity faces ‘grand challenges’ of unprecedented scale, interrelatedness and complexity such as climate change and poverty, management research is joining global efforts to understand these challenges. Both the responsible management and sustainability literatures are well positioned to join these efforts, given that they seek to explore and enable managerial practices that balance social, environmental and economic goals. In particular, the sustainability literature has begun adopting a paradox lens for examining the tensions inherent in balancing these often disparate goals. A paradox perspective approaches tensions as contradictory, interrelated and persistent, and seeks ways to manage these tensions productively. In this chapter, we explore how a paradoxical approach to sustainability tensions has important relevance to responsible management practices for addressing grand challenges.