Despite many recent advances in sustainability science, researchers still struggle to address the key characteristics of social-ecological systems that underlie many of today's problems. Complex cross-scale dynamics and tightly interrelated social and ecological processes characterize social-ecological systems (SES). These features lead to constant change and novelty. Process philosophers argue that the difficulties of capturing these features may have their roots in our tendency to understand the world in terms of substances. This tendency is a legacy of dominant philosophical views that, although now debunked, continue to inform (albeit mostly implicitly) our explanations of reality. These philosophical views are based on the primacy of fundamental entities and stability, which is in contradiction to the continuously changing nature of SES. In this paper, we demonstrate that adopting a process-relational perspective, which focuses on nonequilibrium dynamics and relations between processes, provides novel opportunities to advance SES research. We propose concrete steps toward developing a process-relational perspective of SES and discuss how such a perspective can help us to overcome the challenges currently facing SES research.