This paper explores the role of regulatory sandboxes as tools to foster ethical and responsible innovation in artificial intelligence (AI) systems and discusses the synergies of sandboxes with responsive regulatory theory. The analysis is carried out through bibliographical research with focus on experiences from the Global South (Brazil, Colombia, and Singapore) and European countries. To argue about the importance of sandboxes as drivers for ethical innovation in AI, the study (i) starts from sandboxes based on sectoral regulatory licensing regimes, such as the financial and telecommunications sectors, (ii) advances to the experiments carried out in regulatory regimes based on risk and fundamental rights protection, such as personal data protection, and (iii) analyses the legislative debates on regulatory sandboxes in the contexts of AI regulation in the European Union and in Brazil, in order to reflect which of the previous approaches AI sandboxes are closest to. Finally, (iv) the study reflects on the synergies of sandboxes with the theory of responsive regulation, so that they can be integrated into regulatory strategies which adopt this theory.