The article gives a definition of Big Data on the basis of 5V (Volume, Variety, Velocity, Veracity, Value) as well as shows examples of tasks that require using Big Data tools in a diversity of areas, namely: health, education, financial services, industry, agriculture, logistics, retail, information technology, telecommunications and others. An overview of Big Data tools is delivered, including open source products, IBM Bluemix and SAP HANA platforms. Examples of architecture of corporate data processing and management systems using Big Data tools are shown for big Internet companies and for enterprises in traditional industries. Within the overview, a classification of Big Data tools is proposed that fills gaps of previously developed similar classifications. The new classification contains 19 classes and allows embracing several hundreds of existing and emerging products.

The uprise and use of Big Data tools, in addition to solving practical problems, affects the development of scientific disciplines concerning the simulation of technical, natural or socioeconomic systems and the solution of practical problems based on developed models. New schools arise in these disciplines. These new schools decide peculiar to each discipline tasks, but for systems with a much bigger number of internal elements and connections between them. Characteristics of the problems to be solved under new schools, not always meet the criteria for Big Data. It is suggested to identify the Big Data as a part of the theory of sorting and searching algorithms. In other disciplines the new schools are called by analogy with Big Data: Big Calculation in numerical methods, Big Simulation in imitational modeling, Big Management in the management of socio-economic systems, Big Optimal Control in the optimal control theory. The paper shows examples of tasks and methods to be developed within new schools. The educed tendency is not limited to the considered disciplines: there are other ones such as graph theory, mathematical statistic, game theory, and operations research.