The analysis and interpretation of past climate data and simulations of climate models for future periods will allow us to study the impacts of climate change on cultural Heritage. The H2020 SCORE project (Sustainable COnservation and REstoration of built cultural heritage – 2020-2024) centres on two types of cultural heritage that differ by their geographical location and therefore their climatic conditions, as are vernacular cultural heritage in Europe (6 sites in Denmark, France, Italy and Spain) and archaeological sites in Latin America (2 sites in Mexico). All the cases study share a fundamental similarity in terms of the use of materials and construction techniques. One objective of the project is to quantify the impacts of continuous climate and pollution changes on building materials of cultural heritage under future IPCC socioeconomic scenarios with high and low mitigation measures at years 2030, 2050 and 2070, using peer-reviewed dose-response equations. We also focus on the degradation effects due to extreme events (heatwave, dry spells and extreme rainfall/flood) of each of the selected regions of our cases study. We apply these climatic conditions past and future) in different models, based on scientific literature, that allow estimate the weathering of the materials employed in the construction of cultural heritage buildings. Finally, we deliver preliminary results for a “cocktail of extreme events” based on the literature review and experiment in laboratory specifically designed to quantify the damages and degradation of building materials due to a realistic series of adverse climate and pollution events. We present here some results of future weathering (2081-2100) compared to near par (2001-2020) for different weathering process under the SSP5- RCP 8.5 scenario. The evolution of each process is different and it is different form one site to the other.