Already by the 18th century, damage to natural building stones by sulfur emitting burning coal was described. A table is presented classifying the formation, structure and properties of these stones. Water absorption is extensively dealt with by analyzing the porosity of the material, the osmotic and hydrostatic pressure, the influence of wind pressure and the relative humidity of the atmosphere. Weathering depends on the exchange between heterogeneous systems, the lithosphere, atmosphere, hydrosphere as well as the biosphere. Relevant properties and their interactions are described. Physical influences like temperature variations, water exchange, frost and thawing as well as reactions with salts, sulfates, nitrates, chlorides, and carbonates are extensively analyzed.