The impact of big data technologies on children's data protection is very important. First of all because of children's vulnerability, due their lack of knowledge about the risks of an inadequate data management and, secondly, because the immense possibilities of traceability of a child or a group of children. Consequently, the negative effects in terms of future discrimination for their social and political participation, employability, usability of services, etc., could be immense. Europe has a new Law on protection of personal data (UE2016/679). This paper examines in which way the Law pays attention to this particular area of protection of children. In order to value the proposals of the European Law, this paper studies comparatively some of the reports of the Working Group, art. 29, and the US law Children's online personal data protection act (Coppa).