Due to the advances in the digitalization process of the manufacturing industry and the resulting available data, there is tremendous progress and large interest in integrating machine learning and optimization methods on the shop floor in order to improve production processes. Additionally, a shortage of resources leads to increasing acceptance of new approaches, such as machine learning to save energy, time, and resources, and avoid waste. After describing possible occurring data types in the manufacturing world, this study covers the majority of relevant literature from 2008 to 2018 dealing with machine learning and optimization approaches for product quality or process improvement in the manufacturing industry. The review shows that there is hardly any correlation between the used data, the amount of data, the machine learning algorithms, the used optimizers, and the respective problem from the production. The detailed correlations between these criteria and the recent progress made in this area as well as the issues that are still unsolved are discussed in this paper.