In a world mediated by algorithms, in which decision-making spaces previously destined for humans are now dominated by these artifacts, urges a demand for these algorithmic decisions to be explainable. This challenge gains a layer of complexity when artificial intelligence techniques are used, in particular, the application of machine learning models, given the opacity and inscrutability of the operating mode and the results generated by some types of these algorithms. In this sense, this thesis begins with the presentation of the concept and challenges of artificial intelligence and machine learning for the area of Law, particularly for fundamental rights (i.e. data protection, privacy, freedom, autonomy and equality). Then, the discussion involving the arise of a right to explanation is presented, and how its provision in the LGPD can be interpreted in the light of the lessons learned and interpretations already gathered under the GDPR. Furthermore, it will be analyzed how the main challenges for fundamental rights that are posed by such decision-making algorithms can be summarized under the principles of transparency, accountability and justice/equality. A multifaceted and multidisciplinary approach is proposed, to be applied at different moments in time, to ensure that such principles are incorporated during the development and use of machine learning decision-making algorithms. Finally, this thesis proposed that guaranteeing a right to explanation, which is currently allocated in a broader discussion involving accountability, must take into account a perspective of merit and procedure. The different types of content that have been mapped as likely to be required as an explanation are identified, as well as the values and rights that a right to explanation aims to protect, demonstrating, finally, the importance that such content be subject to public scrutiny.