A series of recent developments points towards auditing as a promising mechanism to bridge the gap between principles and practice in AI ethics. Building on ongoing discussions concerning ethics-based auditing, we offer three contributions. First, we argue that ethics-based auditing can improve the quality of decision making, increase user satisfaction, unlock growth potential, enable law-making, and relieve human suffering. Second, we highlight current best practices to support the design and implementation of ethics-based auditing: To be feasible and effective, ethics-based auditing should take the form of a continuous and constructive process, approach ethical alignment from a system perspective, and be aligned with public policies and incentives for ethically desirable behaviour. Third, we identify and discuss the constraints associated with ethics-based auditing. Only by understanding and accounting for these constraints can ethics-based auditing facilitate ethical alignment of AI, while enabling society to reap the full economic and social benefits of automation.