Artificial intelligence (AI) is increasingly shaping the decisions that affect our lives—from hiring and education to healthcare and access to social services. While AI promises efficiency and objectivity, it also carries the risk of perpetuating and even amplifying societal biases embedded in the data used to train these systems. Many real-world examples highlight the dangers of relying on automated decision-making, as these algorithms can reinforce existing inequalities and discrimination. In this talk, I will explore some challenges of algorithmic fairness. I will begin by discussing the origins of bias in algorithms, as well as their impact on machine learning algorithms. I will then present some of the main approaches used to define, study and enforce algorithmic fairness. In a second part of the talk, I will focus more specifically on the statistical fairness framework, and present some classical results regarding the problem of fair regression. Specifically, I will focus on the criterion of Demographic Parity and examine the relationship between optimal predictions in the contexts of fair classification and fair regression.