As the Internet has become a mainstream communications mechanism, law enforcement and intelligence agencies have developed new surveillance capabilities and been given new legal powers to monitor its users. These capabilities have been particularly targeted toward terrorism suspects and organizations that have been observed using the Internet for communication, propaganda, research, planning, publicity, fundraising and creating a distributed sense of community. Policing has become increasingly pre-emptive, with a range of activities criminalized as 'supporting' or 'apologizing for' terrorism. The privacy and non-discrimination rights that are core to the European legal framework are being challenged by the increased surveillance and profiling of terrorism suspects. We argue that their disproportionate nature is problematic for democracy and the rule of law, and will lead to practical difficulties for cross-border cooperation between law enforcement agencies.