The development of artificial intelligence (AI) has made various industries eager to explore the benefits of AI. There is an increasing amount of research surrounding AI, most of which is centred on the development of new AI algorithms and techniques. However, the advent of AI is bringing an increasing set of practical problems related to AI model lifecycle management that need to be investigated. We address this gap by conducting a systematic mapping study on the lifecycle of AI model. Through quantitative research, we provide an overview of the field, identify research opportunities, and provide suggestions for future research. Our study yields 405 publications published from 2005 to 2020, mapped in 5 different main research topics, and 31 sub-topics. We observe that only a minority of publications focus on data management and model production problems, and that more studies should address the AI lifecycle from a holistic perspective.