Explanations have gained an increasing level of interest in the AI and Machine Learning (ML) communities in order to improve model transparency and allow users to form a mental model of a trained ML model. However, explanations can go beyond this one way communication as a mechanism to elicit user control, because once users understand, they can then provide feedback. The goal of this paper is to present an overview of research where explanations are combined with interactive capabilities as a mean to learn new models from scratch and to edit and debug existing ones. To this end, we draw a conceptual map of the state-of-the-art, grouping relevant approaches based on their intended purpose and on how they structure the interaction, highlighting similarities and differences between them. We also discuss open research issues and outline possible directions forward, with the hope of spurring further research on this blooming research topic.