This paper takes a rate-distortion approach to understanding the information-theoretic laws governing cache-aided communications systems. Specifically, we characterise the optimal tradeoffs between the delivery rate, cache capacity and reconstruction distortions for a single-user problem and some special cases of a two-user problem. Our analysis considers discrete memoryless sources, expected- and excess-distortion constraints, and separable and f-separable distortion functions. We also establish a strong converse for separable-distortion functions, and we show that lossy versions of common information (Gács-Körner and Wyner) play an important role in caching. Finally, we illustrate and explicitly evaluate these laws for multivariate Gaussian sources and binary symmetric sources.