This chapter discusses the ethical complications and challenges arising from the use of AI systems in our everyday lives. It outlines recent and upcoming regulations and policies regarding the use of AI systems, and dives into the topics of explainability and fairness. We argue that trustworthiness has at its heart explainability, and thus we present ideas and techniques aimed at making AI systems more understandable and ultimately more trustworthy for humans. Moreover, we discuss the topic of algorithmic fairness and the requirement that AI systems are free from biases and do not discriminate against individuals on the basis of some protected attributes. In all cases, we present a brief summary of the most important concepts and results in the literature. As a conclusion, we present some ideas for future research and sketch open challenges in the field.