This paper gives a description of the implementation of the institution of inheritance mortis causa at the international level especially at the European level, based on the new European directive, the Regulation No. 650/2012 which entered into force on August 17, 2015. This paper deals with those aspects that relate with the regulation of the inheritance relationship in private international law, the applicable law, the circulation of court decisions and public acts, their recognition and applicability and the newest act that this regulation has brought, the "European Certificate of Justice", with all its elements which is applied in all countries European and aimed to achieve the highest objective of the European legislator, which is none other than harmonization, unification and international coordination in the field of private law. In the conclusions and recommendations, are identified the main issues where there have been difficulties in the implementation of the institution of inheritance in the EU countries and the definition of common practices for the implementation of this institution have been proposed.