Global warming is associated with increasingly widespread and frequent climate extremes. This paper develops a dynamic stochastic multi-region model of consumption smoothing, storage, and trade to investigate the buffering effect of agricultural markets in the context of climate extremes. The theory provides new insights on the impact of household market transaction costs, borrowing constraints and the spatiotemporal pattern of climate shocks. A large-scale empirical analysis of market access, climate extremes, and food insecurity at quarterly subnational level in Sub-Saharan Africa supports the theoretical predictions. Regions with shorter travel times to cities and ports experience a smaller detrimental impact on food insecurity from severe and extreme dry conditions. Trade and storage appear partly substitutes in buffering the food insecurity impacts of country-wide and multi-year climate extremes.