Algorithms bring both economic and social benefits and can help fight social inequalities. However, they do not escape the ambivalence that characterizes technological progress: they can cause discrimination and marginalization. After disproving the myth of algorithmic infallibility and neutrality, the paper brings to attention some examples of algorithmic discrimination that have occurred in public activity. Once the issue has been exemplified, it investigates how discriminatory algorithms are generated (however, these mechanisms are not entirely perspicuous and this lack of clarity is itself part of the problem). Finally, the paper focuses on the solutions given by law, with particular reference to the algorithmic decision-making principles of the GDPR and the proposed EU regulation on artificial intelligence. Since the current regulatory system, as well as those envisaged in the future, have inherent limitations due to the speed and unpredictability of technological developments, the analysis concludes by underlining the need for a responsible education both of developers, who design algorithms, and of users of digital instruments.