This talk will be based on two recent papers. In the first one "The Fairness of Machine Learning in Insurance: New Rags for an Old Man?" (co-author Laurence Barry), we present an overview of issues actuaries face when dealing with discrimination. Since the beginning of their history, insurers have been known to use data to classify and price risks. As such, they were confronted early on with the problem of fairness and discrimination associated with data. This issue is becoming increasingly important with access to more granular and behavioural data, and is evolving to reflect current technologies and societal concerns. By looking into earlier debates on discrimination, we show that some algorithmic biases are a renewed version of older ones, while others seem to reverse the previous order. Paradoxically, while the insurance practice has not deeply changed nor are most of these biases new, the machine learning era still deeply shakes the conception of insurance fairness. In the second one "A fair pricing model via adversarial learning" (co-authors Vincent Grari, Sylvain Lamprier and Marcin Detyniecki), we suggest a technique to construct a fair pricing model using maximal correlation based techniques and adversarial learning.