Understanding and managing stone decay and soiling pose huge challenges to scientists, conservators, building managers and architects. Despite decades of study and practical experience there are still great gaps in our knowledge of how decay and soiling work. Oxford provides a good example of the range of problems faced. Much of Oxford's cultural heritage is made from a suite of Jurassic building limestones prone to decay and soiling. Such decay and soiling are complex problems involving a web of interacting processes exhibiting considerable variation over both space and time. Cause-effect links are often very hard to elucidate, and may appear different at different scales and depending on the analytical methods used. Information from a range of experimental, monitoring and modelling studies carried out over the past 6 years in Oxford indicates the potential value of adopting non-linear dynamical systems approaches to understanding stone decay. Acknowledging the non-linear nature of stone decay has implications for management and conservation practice.