Artificial intelligence is being implemented in an increasing number of areas, among which healthcare, finance and justice, with the aim of using it as decision-making support. However, high-performing models are usually not trusted by the final user, since they are not transparent. Understanding the model behaviour is fundamental, especially in critical tasks, but it is not enough to build AI systems that have the well-being of humans in the first place. To understand what AI needs to be trustworthy, the concept of responsibility in the Artificial Intelligence field is introduced. It is analyzed in detail, considering all the components needed to build a Responsible Artificial Intelligence system, from explainability to fairness, passing through accountability, security, inclusiveness and reliability.