The purpose of this paper is to study and understand emergent process of the right to erasure personal data in internet search within Spanish Law and its subsequent incorporation into European Community Law. In this, this work sustains that this right to suppression is the result of various legal causes framed in the need to protect personal data, privacy and other related rights. Likewise, the case that constituted the starting point for the reform of the data, Costeja-AEPD v. Google Spain, S.L., Google Inc protection system, is presented in the General Data Protection Regulation in European Community Law. Finally, the way that right to erasure has been recognized in current European Communitarian Law is exposed.