The structural instability of grottoes and stone heritage buildings is mostly attributed to the decline in mechanical properties and stability of their key load-bearing components under long-term weathering effects. The stability and the evolution process of instability of these structures are closely related to the stress conditions of the key load-bearing components and the deterioration patterns of their mechanical properties due to weathering. Based on a comprehensive review of the research status on the main problems involved in the stability and durability studies of such grottoes and ancient stone architectures (including the weathering depth of stone components and the determination method of mechanical parameters of weathering layer, the variation law of mechanical parameters with depth in weathering layer, the variation law of weathering depth with time, the evaluation method of stability and durability, etc.), this paper systematically explores potential solutions to address these key scientific and technical challenges. Solutions to the aforementioned problems are briefly introduced through a case study of the stability and durability of the Guyue Bridge in Yiwu built in the Song Dynasty. The methods presented in this article have reference significance for the research on the stability and durability of grottoes and ancient stone architectures.