Information technologies in general and artifical intelligence (AI) in particular try to shift operational task away from a human actor. Machine learning (ML) is a discipline within AI that deals with learning improvement based on data. Subsequently, retailing and wholesaling, which are known for their high proportion of human work and at the same time low profit margins, can be regarded as a natural fit for the application of AI and ML tools. This article examines the current prevalence of the use of machine learning in the industry. The paper uses two disparate approaches to identify the scientific and practical state-of-the-art within the domain: a literature review on the major scientific databases and an empirical study of the 10 largest international retail companies and their adoption of ML technologies in the domain are combined with each other. This text does not present a prototype using machine learning techniques. Instead of a consideration and comparison of the particular algorythms and approaches, the underling problems and operational tasks that are elementary for the specific domain are identified. Based on a comprehensive literature review the main problem types that ML can serve, and the associated ML techniques, are evaluated. An empirical study of the 10 largest retail companies and their ML adoption shows that the practical market adoption is highly variable. The pioneers have extensively integrated applications into everyday business, while others only show a small set of early prototypes. However, some others show neither active use nor efforts to apply such a technology. Following this, a structured approach is taken to analyze the value-adding core processes of retail companies. The current scientific and practical application scenarios and possibilities are illustrated in detail. In summary, there are numerous possible applications in all areas. In particular, in areas where future forecasts and predictions are needed (like marketing or replenishment), the use of ML today is both scientifically and practically highly developed.