In this article, we describe the implementation of algorithms based on machine learning for personnel selection procedures and how this data-driven approach corresponds to and differentiates from classical psychological assessment. We discuss if, and in what way, bias and discrimination occur when using algorithms based on machine learning for personnel selection. For this reason, we conducted a literature review (covering 2016-2019) from which 41 articles were included. The results indicate that algorithms possibly lead to reduced (indirect) discrimination compared to some other selection methods. This is one of the reasons why the development of algorithms for personnel selection has increased quickly and the number of vendors has grown fast. It is insufficiently possible yet, however, to ascertain if the promise is kept. First, this is because algorithms are often trade secrets (lack of transparency). Second, the validity and reliability of data used for the development of algorithms are not always clear. Furthermore, psychological selection issues about diversity and validity cannot (yet) be solved by algorithms. The increasing attention for the topic, expressed by a large growth in publications, is hopeful. We conclude with recommendations for the detection and reduction of bias and discrimination when using machine learning algorithms for personnel selection.