The preservation of heritage is crucial to successfully accomplish the Sustaining Development Goals (SDGs) because it leads to social unity; therefore, evaluating the decay mechanisms of stone-built heritage sites is critical to understanding the role of atmospheric conditions towards their conservation and to developing effective policies in the preservation of heritage and hence, community strength. In this paper, the differences of material decay between Italy’s and Mexico’s atmospheres and the perspectives to implement a more active role of the atmospheric sciences in the conservation of built heritage are presented. The risk assessment methodology proposed by the International Center for the Study of the Preservation and Restoration of Cultural Property (ICCROM) is used to present the reviewed published research because it is one of the few methodologies suggested for amply analyzing cultural property. Currently, in Europe, most research is aimed either to estimate the future decay of built property or to assess the main threats to a single site, on sites for which building materials have been studied previously and on sites for which forecast models have been developed, and the results are useful towards a preventive conservation approach, although the damage functions were developed considering a single climate and might not perform well under different conditions. Built property, however, is present worldwide and the conditions of those studies are not met in most developing countries, as the variation in materials and atmospheric conditions has not been researched yet. This article intends to reduce this gap by comparing both approaches, acknowledging possible common courses of action, and highlighting the role of built heritage in SDGs.