The world faces a multiplicity of global catastrophic risks (GCRs), whose functionality as individual and collective complex adaptive networks (CANs) poses unique problems for governance in a world that itself comprises an intricately interlinked set of CANs. Here we examine necessary conditions for new approaches to governance that consider the known properties of CANs-especially that small changes in one part of the system can cascade and amplify throughout the system and that the system as a whole can also undergo rapid, dramatic, and often unpredictable change with little or no warning.