Organizations in various industries have widely developed the artificial intelligence (AI) maturity model as a systematic approach. This study aims to review state-of-the-art studies related to AI maturity models systematically. It allows a deeper understanding of the methodological issues relevant to maturity models, especially in terms of the objectives, methods employed to develop and validate the models, and the scope and characteristics of maturity model development. Our analysis reveals that most works concentrate on developing maturity models with or without their empirical validation. It shows that the most significant proportion of models were designed for specific domains and purposes. Maturity model development typically uses a bottom-up design approach, and most of the models have a descriptive characteristic. Besides that, maturity grid and continuous representation with five levels are currently trending in maturity model development. Six out of 13 studies (46%) on AI maturity pertain to assess the technology aspect, even in specific domains. It confirms that organizations still require an improvement in their AI capability and in strengthening AI maturity. This review provides an essential contribution to the evolution of organizations using AI to explain the concepts, approaches, and elements of maturity models.