How to investigate algorithmic-driven risks in online platforms and search engines? A narrative review through the lens of the EU Digital Services Act

Algorithmic systems are increasingly integrated into digital services, where they shape user experiences, mediate access to information, and influence decision-making processes. As their societal impact grows, the field of algorithm auditing has emerged in recent years as a specialized area of study and practice focused on examining how these systems operate and assessing their broader impact on society. On the regulatory side, the European Union's Digital Services Act (DSA) introduces new obligations for digital services, including provisions that specifically address the algorithms employed by very large online platforms and search engines. This paper seeks to establish a connection between the field of algorithm auditing and the provisions of the DSA that specifically address algorithmic systems. We analyze the existing algorithm auditing literature and develop a taxonomy of study designs, defined as structured plans used to investigate risks associated with the use, design, and functioning of digital services's algorithms. We categorize these study designs based on their objectives in the broad risk management framework of the DSA, and identify key methodological steps and best practices. In doing so, this paper offers a guide for researchers, auditors, and digital services aiming to adopt rigorous approaches to algorithm auditing within the framework of the DSA.