Dealing consistently with risk and uncertainty across the IPCC reports is a difficult challenge. Huge practical difficulties arise from the Panel's scale and interdisciplinary context, the complexity of the climate change issue and its political context. The key question of this paper is if the observed differences in the handling of uncertainties by the three IPCC Working Groups can be clarified. To address this question, the paper reviews a few key issues on the foundations of uncertainty analysis, and summarizes the history of the treatment of uncertainty by the IPCC. One of the key findings is that there is reason to agree to disagree: the fundamental differences between the issues covered by the IPCC's three interdisciplinary Working Groups, between the type of information available, and between the dominant paradigms of the practitioners, legitimately lead to different approaches. We argue that properly using the IPCC's Guidance Notes for Lead Authors for addressing uncertainty, adding a pedigree analysis for key findings, and particularly communicating the diverse nature of uncertainty to the users of the assessment would increase the quality of the assessment. This approach would provide information about the nature of the uncertainties in addition to their magnitude and the confidence assessors have in their findings.