Many impacts of climate change will be realised as the result of a change in the frequency of occurrence of extreme weather events. Thus a specific research objective of the Tyndall Centre is to estimate past and future probabilities of selected extreme weather events and rapid climate changes. This is the focus of Tyndall Project IT1.16, during which, this working paper was produced. The starting point for a comprehensive assessment of methods that are most suitable for the estimation of future probabilities of extreme weather events is recent work on scenario development methods, including that reported in the IPCC Third Assessment Report, which is outlined in the paper. In order to assess the most suitable methods, it is first important to identify the range of scenario information that is required by stakeholders and others with requirements for climate change impact assessments. A number of relevant questions and topics, including issues which are particularly relevant to the need to develop probabilistic approaches and integrated assessment models, are presented, together with a list of proposed indicators of temperature and rainfall weather extremes. A number of potential scenario development methods are identified. These fall into three main categories: direct use of global climate model output; direct use of regional climate model output; and, statistical downscaling of climate model output. The limitations of each are evaluated, both generally, and for the specific problems of inter-annual variability, multi-variate correlations, multi-site correlations, spatial-scale dependence and scaling by simple models to obtain a range of scenarios. Consideration is also given to the evaluation and incorporation into assessment studies of low probability, but high impact events, focusing on an abrupt reorganisation of the North Atlantic thermohaline circulation. There are two aspects of such events that must be addressed: (i) the possibility of the event occurring, and (ii) the response of the climate system to the event. All the necessary questions concerning scenarios of extreme events cannot be answered on the basis of past work and the critical reviews presented here alone. Thus specific applications to test cases will be undertaken as part of the project in order to rigorously and, where possible, quantitatively, compare and evaluate the various methods, and to further develop methods in order to overcome the identified problems. Two selected case studies are outlined. The first, focuses on drought. The second, is based on changes in the intensity of daily precipitation, but will focus on joint probability events, i.e., the joint probability of high river flows, high tides and storm surges. A draft version of this working paper formed the basis of discussion at the project workshop held in Norwich in June 2001. A number of additional issues which arose during the workshop discussions, relating to indicators of extremes, methodological approaches and case studies, are summarised in the Appendix.