The aim of this paper is to define cloud data storage, determine key differences between traditional data storage and cloud data storage and to determine their advantages and disadvantages, as well as highlight the economic differences between the two methods. Cloud data storage is one of the services of Cloud computing, it is based on the idea that data isn't stored on the user's computer, rather than that the user has to use the Internet to access his data. Primary benefits of cloud storage over traditional storage are flexibility of accessing stored data for which the only requirement is an Internet connection, adapting to the changing and growing demands for storage space and a large number of services providing cloud computing services to meet customer needs. Cloud storage is an increasingly common storage method, especially in business which through its use generates significant financial savings by eliminating the need for infrastructure, maintaining and hiring professional staff. The paper consists of an introduction, eleven main chapters, and conclusion. Through the first four chapters the goal is to get to know more about cloud computing, types of cloud computing (private, public, hybrid and community cloud), models of delivering the cloud service (IaaS, PaaS, SaaS), history of cloud computing and it's advantages and disadvantages. Then follow the chapters on traditional data storage and cloud data storage, their differences, services that provide data storage, the economic aspect of cloud data storage, businesses that migrated to cloud and the last chapter on the future of cloud storage.