The development and extensive use of highly distributed and scalable systems to process Big Data have been widely considered. New data management architectures, e.g. distributed file systems and NoSQL databases, are used in this context. However, features of Big Data like their complexity and data analytics demands indicate that these concepts solve Big Data problems only partially. A development of so called NewSQL databases is highly relevant and even special category of Big Data Management Systems is considered. In this work we will discuss these trends and evaluate some current approaches to Big Data processing, identify the current challenges, and suggest possible research directions.