There is an acknowledged need for improved conservation of plastic and rubber objects within collections, including improved methods of condition assessment, material identification, and better understanding of material degradation. This reflects the inherent instability and wide-ranging formulations of many such objects and also the relative lack of knowledge in this field. Analysis of volatile organic compounds (VOCs) is a useful method for understanding the chemical processes involved in polymer degradation and for the identification of materials. Conservators and curators have used odor analysis to identify historical plastics for many years, and techniques ranging from acid detection strips to laboratory-based techniques such as solid-phase microextraction-gas chromatography-mass spectrometry have been used to characterize plastic and rubber materials and to understand their degradation. VOC analysis also has potential as a technique for bulk material identification, as a complementary tool to spectroscopic analysis of the surface. A significant advantage of VOC analysis is its potential to be non-invasive, avoiding destructive sampling or even contact with an object. However, there is a greater potential for VOC analysis to be of benefit within conservation than is currently being exploited and significant scope for future research. In fields such as construction or waste management, there is also significant research into analysis of VOC emissions from plastic and rubber materials. The goal of this paper is to systematically review research from a range of fields including conservation, polymer degradation, and plastics recycling and it includes the use of VOC analysis to understand the causes of damage to plastic and rubber objects, to provide evidence of degradation and to monitor degradation progress, and to identify materials and distinguish between different formulations. Summaries of relevant studies are given, and volatile markers of object damage and polymer degradation and key volatile identifiers of a particular material are highlighted.