As artificial intelligence (AI) systems are increasingly deployed, principles for ethical AI are also proliferating. Certification offers a method to both incentivize adoption of these principles and substantiate that they have been implemented in practice. This paper draws from management literature on certification and reviews current AI certification programs and proposals. Successful programs rely on both emerging technical methods and specific design considerations. In order to avoid two common failures of certification, program designs should ensure that the symbol of the certification is substantially implemented in practice and that the program achieves its stated goals. The review indicates that the field currently focuses on self-certification and third-party certification of systems, individuals, and organizations - to the exclusion of process management certifications. Additionally, the paper considers prospects for future AI certification programs. Ongoing changes in AI technology suggest that AI certification regimes should be designed to emphasize governance criteria of enduring value, such as ethics training for AI developers, and to adjust technical criteria as the technology changes. Overall, certification can play a valuable mix in the portfolio of AI governance tools.