Auditing algorithms, to assess risks that they pose, is an increasingly important theme in governing technologies. Audits play a key role in the EU’s new Digital Services Act (DSA), and implementation is currently the subject of extensive discussion. These experiences will inform the upcoming AI Act, and other legislation worldwide. New institutions including the European Centre for Algorithmic Transparency (ECAT), and AI Safety Institutes in countries including the UK and US, are important steps in developing specialised expertise and new methods. However alongside these developments, fundamental questions remain. Amongst these are: What should actually be measured, and how? How to capture social, as well as technical, issues? What are thresholds for unacceptable risk? How to balance collaboration and independence during audits? This panel will hear how existing approaches in auditing, plus new methods in algorithmic investigations, can address these challenges.