This review is conceived as a guide for material science researchers and conservators aiming to face the problem of deterioration of contemporary artworks entirely or partially made of plastics. It initially illustrates the analytical approaches for identifying polymeric material components in 3D art objects, such as sculptures and installations, and provides a perspective of their limits and advantages. Subsequently, the methodologies used for studying the deterioration of contemporary art plastics are reviewed, emphasising the main effects of the different types of degradation (i.e., migration of additives, oxidation and hydrolysis) and suggesting the appropriate techniques for their detection. Finally, the application of artificial ageing tests is critically assessed. All the concepts are elaborated through case studies and examples.