There is little doubt that digitalisation is revolutionising many sectors of our economies. Algorithms are among the most important technological drivers of this process and enable firms to be more innovative and efficient. Nevertheless, debate has arisen on whether and to what extent algorithms might have detrimental effects on the competitive functioning of markets, especially by facilitating collusive practices. This joint study by the Autorité de la concurrence and the Bundeskartellamt addresses the potential competitive risks associated with the use of algorithms. It elaborates on the concept of algorithm as well as on different types and fields of application (II.) and subsequently focusses on algorithms and collusion (III.). After that, the study discusses practical challenges when investigating algorithms (IV.) and concludes with a tentative outlook for the tasks of competition authorities deriving from the study (V.).