Slow-Developing Catastrophic Risks (SDCRs) refer to risks, the development of which, though hardly discernible at first or by non-experts, may lead to critical transitions (or regime shifts). As a result, SDCRs can have catastrophic consequences in terms of fatalities or economic losses. Because of their non-imminence and uncertain consequences in the case of critical transitions, it is a challenge for policy makers to deal with them effectively. This review paper synthesizes the key governance issues for SDCRs identified during two multi-stakeholder workshops organised by the International Risk Governance Council, supplemented by literature review of scientific underpinnings and supported by illustrations of real-life SDCRs. The review is organised in three parts, focussing on the evaluation, management, and governance aspects of SDCRs, respectively.