The rapid development of new information technologies and data analytics has caused the awareness of the economic value of data and data has become a new kind of asset. In European union, the acceptance of data as a new legal object is not revolutionary, but a change in the conception of ownership. By introducing data as the vital resource of the digital economy, the improvement of legal rules, including ownership rights, becomes necessary. This paper discusses the concept of data, identifies the challenges in defining the property rights in data by analyzing for and against arguments, and studies the position of data in intellectual property rights, trade secrets, data protection, contracts, and competition law. Attitudes towards ownership as a fundamental concept, in relation to data, face various uncertainties, and focuses on data ownership could arise new economic concerns and legal issues. However, the lack of legal rules on data ownership should no longer be ignored. The mentioned legal systems also do not provide a sufficient basis for ownership of data. The solution is to regulate data, based on a clear definition of ownership while respecting the fundamental rights of individual, and providing the means of success in the digital economy.