Complex systems science provides a transdisciplinary framework to study systems characterized by (1) heterogeneity, (2) hierarchy, (3) self-organization, (4) openness, (5) adaptation, (6) memory, (7) non-linearity, and (8) uncertainty. Complex systems thinking has inspired both theory and applied strategies for improving ecosystem resilience and adaptability, but applications in forest ecology and management are just beginning to emerge. We review the properties of complex systems using four well-studied forest biomes (temperate, boreal, tropical and Mediterranean) as examples. The lens of complex systems science yields insights into facets of forest structure and dynamics that facilitate comparisons among ecosystems. These biomes share the main properties of complex systems but differ in specific ecological properties, disturbance regimes, and human uses. We show how this approach can help forest scientists and managers to conceptualize forests as integrated social-ecological systems and provide concrete examples of how to manage forests as complex adaptive systems.