Artificial Intelligence systems are spreading to multiple applications and they are used by a more diverse audience. With this change of the use scenario, AI users will increasingly require explanations. The first part of this paper makes a review of the state of the art of Explainable AI and highlights how the current research is not paying enough attention to whom the explanations are targeted. In the second part of the paper, it is suggested a new explainability pipeline, where users are classified in three main groups (developers or AI researchers, domain experts and lay users). Inspired by the cooperative principles of conversations, it is discussed how creating different explanations for each of the targeted groups can overcome some of the difficulties related to creating good explanations and evaluating them.