The guiding observation behind this report is that despite attracting considerable attention, populist extremist parties and their supporters remain poorly understood. This is largely because debates about this challenge have often failed to engage with a large body of evidence on these parties, their supporters and their motivations. Taking an evidence-based approach, this report draws on a series of workshops that were organized in four countries and investigated eight cases of populist extremism. These brought together academic experts, members of national parliaments and the European Parliament, and civil society groups to start closing the gaps between debate, policy and evidence. Specifically, the report is concerned with three areas: (1) the profile and motivations of PEP supporters, (2) the message that PEPs offer and the extent to which citizens in Europe are receptive, and (3) potential response strategies.