There is much debate whether hard-hitting legal regulation with respect to AI and big data is required. Our research shows that the danger with this is its potential to cause unforeseen, adverse or chilling effects that are unintended in a field that is very dynamic and fast-developing. There are various proposals for laws, regulatory bodies and other regulatory tools and mechanisms to support, enhance or monitor the responsible development of AI and big data technologies. This briefing, focusing particularly on the EU-level, presents snapshots of policy and other stakeholder perspectives on the regulation of AI, regulatory options and recommendations on potential courses of action based on SHERPA research.