The main problems faced by scientists in working with Big Data sets, highlighting the main ethical issues, taking into account the legislation of the European Union. After a brief Introduction to Big Data, the Technology section presents specific research applications. There is an approach to the main philosophical issues in Philosophical Aspects, and Legal Aspects with specific ethical issues in the EU Regulation on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing Directive 95/46/EC (Data Protection Directive - General Data Protection Regulation, "GDPR"). The Ethics Issues section details the specific aspects of Big Data. After a brief section of Big Data Research, I finalize my work with the presentation of Conclusions on research ethics in working with Big Data.