This note investigates fairness in insurance pricing, focusing on two complementary notions: proxy discrimination and demographic parity. Proxy discrimination arises when apparently neutral risk factors encode information about protected attributes, leading to indirect and often unintended discrimination. Demographic parity, by contrast, is a group fairness criterion requiring the distribution of premiums to be independent of protected characteristics. We discuss the conceptual differences between these two approaches. Building on recent contributions of Simon, Denuit and Trufin (2025), we then describe tree-based methods (the DPTree and its ensemble extension, the DPForest) that embed demographic parity constraints directly into predictive models. These methods demonstrate how fairness requirements can be operationalised transparently within standard actuarial tools, while also illustrating the inherent trade-offs between accuracy and fairness.