Systemic climate risks, which result from the potential for cascading impacts through inter-related systems, pose particular challenges to risk assessment, especially when risks are transmitted across sectors and international boundaries. Most impacts of climate variability and change affect regions and jurisdictions in complex ways, and techniques for assessing this transmission of risk are still somewhat limited. Here, we begin to define new approaches to risk assessment that can account for transboundary and trans-sector risk transmission, by presenting: (i) a typology of risk transmission that distinguishes clearly the role of climate versus the role of the social and economic systems that distribute resources; (ii) a review of existing modelling, qualitative and systems-based methods of assessing risk and risk transmission; and (iii) case studies that examine risk transmission in human displacement, food, water and energy security. The case studies show that policies and institutions can attenuate risks significantly through cooperation that can be mutually beneficial to all parties. We conclude with some suggestions for assessment of complex risk transmission mechanisms: use of expert judgement; interactive scenario building; global systems science and big data; innovative use of climate and integrated assessment models; and methods to understand societal responses to climate risk. These approaches aim to inform both research and national-level risk assessment.