The European Commission estimates that more than half of all criminal investigations today involve a cross-border request to access electronic evidence. The globalization of criminal evidence is creating significant challenges for law enforcement. Countries around the world are responding with new laws and legal proposals, which often raise important questions in relation with privacy, human rights, national security and the relations between States. Prominent among them, the Cloud Act, adopted by the US Congress in March 2018, authorizes US law enforcement authorities to obtain from Internet and Cloud providers electronic evidence regardless of the location of data. The EU Commission also presented in April 2018 an important legislative package called “E-Evidence” as a European version of the “Cloud Act”. Which are the legal and policy issues created by these two instruments, and what are the prospects for the conclusion of bilateral data sharing agreements, including between the USA and the EU ?