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Knowledge discovery from temporal, spatial and spatiotemporal data is critical for climate change science and climate impacts. Climate statistics is a mature area. However, recent growth in observations and model outputs, combined with the increased availability of geographical data, presents new opportunities for data miners. This paper maps climate requirements to solutions available in temporal, spatial and spatiotemporal data mining. The challenges result from long-range, long-memory and possibly nonlinear dependence, nonlinear dynamical behavior, presence of thresholds, importance of extreme events or extreme regional stresses caused by global climate change, uncertainty quantification, and the interaction of climate change with the natural and built environments. This paper makes a case for the development of novel algorithms to address these issues, discusses the recent literature, and proposes new directions. An illustrative case study presented here suggests that even relatively simple data mining approaches can provide new scientific insights with high societal impacts.