Climate changes are top biodiversity shapers, both during the past and future. Mapping the most climatic stable and unstable zones on Earth could improve our understanding of biodiversity distribution and evolution. Here, we present a set of maps based on a global scale, high resolution (ca. 5 km) new Climate Stability Index (CSI). The CSI considers bioclimatic variables for two different time ranges: (1) from Pliocene (3.3 Ma) to the present (CSI-past map set), using 12 time periods of PaleoClim representing warm and cold cycles; and (2) from present to the year 2100 (CSI-future), using nine general circulation models of climate change of four periods available from WorldClim. We calculated standard deviation of the variables and selected an uncorrelated set for summing, normalizing and obtaining the CSI maps. Our approach is useful for fields such as biogeography, earth sciences, agriculture, or sociology. However, CSI is an index that can be re-calculated according to particular criteria and objectives (e.g. temperature variables); maps are, therefore, customizable to every user.