With the growing availability of digital administrative data and the recent advances in machine learning, the use of predictive algorithms in the delivery of labour market policy is becoming more prevalent. In public employment services (PES), predictive algorithms are used to support the classification of jobseekers based on their risk of long-term unemployment (profiling), the selection of beneficial active labour market programs (targeting), and the matching of jobseekers to suitable job opportunities (matching). In this chapter, we offer a conceptual introduction to the applications of predictive algorithms for the different functions PES have to fulfil and review the history of their use up to the current state of the practice. In addition, we discuss two issues that are inherent to the use of predictive algorithms: algorithmic fairness concerns and the importance of considering how caseworkers will interact with algorithmic systems and make decisions based on their predictions.