Abstract Non-technical summary Systemic risks such as climate change and pandemics are complex and interconnected. Managing such risks requires effective organisational structures and processes. This publication presents conceptually robust, evidence-based approaches for assessing and managing systemic risks. Technical summary Systemic risks originate and evolve in the nexus of tightly coupled dynamic systems, which are a characteristic of modern societies in the Anthropocene. Systemic risk implies the breakdown of a system which provides essential functions to society. Connectivity between systems is a key enabler for systemic risk to manifest through cascading effects. Thus, systemic risks originate and evolve in the nexus of tightly coupled dynamic systems. Cascading effects and the convergence of systemic risks with conventional risks as well as other systemic risks challenge the established modes of risk governance that still rest to a large extent on differentiation and compartmentalisation. Thus, governance of systemic risks requires an integrative approach towards risk governance that combines interdisciplinary risk analysis with iterative, adaptive and inclusive governance procedures. By drawing on the case studies of the COVID-19 pandemic and climate change, this paper proposes an innovative risk governance framework for systemic risks based on the integration of systems analysis and a governance procedure with the salient features of reflection, iteration, inclusion, transparency and accountability. Social media summary Systemic risks highlight the interconnected nature of our contemporary societies which calls for tailored responses.