Access to online data has long been important for law enforcement agencies in their collection of electronic evidence and investigation of crimes. These activities have also long involved cross-border investigations and international cooperation between agencies and jurisdictions. However, technological advances such as cloud computing have complicated the investigations and cooperation arrangements. Therefore, several new laws have been passed and proposed both in the United States and the European Union for facilitating cross-border crime investigations in the context of cloud computing. These new laws and proposals have also brought many new legal challenges and controversies regarding extraterritoriality, data protection, privacy, and surveillance. With these challenges in mind and with a focus on Europe, this paper reviews the recent trends and policy initiatives for cross-border data access by law enforcement agencies.