Manufacturing companies tend to use standardized delivery times. The actual delivery times requested by the customers and the current capacity utilization of the production are often not taken into account. Therefore, such a simplification likely results in a reduction of the efficiency of the production. For example, it can lead to an obligation to use rush orders, an unrealistic calculation of inventories or an unnecessary exclusion of a Make-to-Order production. In the worst case, this results not only in an economically inadequate production, but also in a low achievement of logistic objectives and therefore in customer complaints. To avoid this, the delivery dates proposed to the customer must be realistic. Given the large number of customer orders, a wide range of products, varying order quantities and times, as well as various delivery times requested by customers, it is not economical to determine individual delivery dates manually. The ongoing digitalization and technological innovations offer new opportunities to support this task. In the literature, various approaches using machine learning methods for specific production planning and control tasks exist. As these methods are in general applicable for different tasks involving predictions, they can also assist during the determination of delivery dates. Therefore, this paper provides a comprehensive review of the state of the art regarding the use of machine learning approaches for the prediction of delivery dates. To identify research gaps the analyzed publications were differentiated according to several criteria, such as the overall objective and the applied methods. The majority of scientific publications addresses delivery dates only as a subordinate aspect while focusing on production planning and control tasks. Therefore, the interrelationships with several production planning and control tasks were considered during the analysis.