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Warming of the Earth climate system is unequivocal. That climate changes affect the stability of natural and engineered slopes and have consequences on landslides, is also undisputable. Less clear is the type, extent, magnitude and direction of the changes in the stability conditions, and on the location, abundance, activity and frequency of landslides in response to the projected climate changes. Climate and landslides act at only partially overlapping spatial and temporal scales, complicating the evaluation of the climate impacts on landslides. We review the literature on landslide-climate studies, and find a bias in their geographical distribution, with large parts of the world not investigated. We recommend to fill the gap with new studies in Asia, South America, and Africa. We examine advantages and limits of the approaches adopted to evaluate the effects of climate variations on landslides, including prospective modelling and retrospective methods that use landslide and climate records. We consider changes in temperature, precipitation, wind and weather systems, and their direct and indirect effects on the stability of single slopes, and we use a probabilistic landslide hazard model to appraise regional landslide changes. Our review indicates that the modelling results of landslide-climate studies depend more on the emission scenarios, the Global Circulation Models, and the methods to downscale the climate variables, than on the description of the variables controlling slope processes. We advocate for constructing ensembles of projections based on a range of emissions scenarios, and to use carefully results from worst-case scenarios that may over/under-estimate landslide hazards and risk. We further advocate that uncertainties in the landslide projections must be quantified and communicated to decision makers and the public. We perform a preliminary global assessment of the future landslide impact, and we present a global map of the projected impact of climate change on landslide activity and abundance. Where global warming is expected to increase the frequency and intensity of severe rainfall events, a primary trigger of rapid-moving landslides that cause many landslide fatalities, we predict an increase in the number of people exposed to landslide risk. Finally, we give recommendations for landslide adaptation and risk reduction strategies in the framework of a warming climate.