The development and extensive use of highly distributed and scalable systems to process Big Data is widely considered. New data management architectures, e.g. distributed file systems and NoSQL databases, are used in this context. On the other hand, features of Big Data like their complexity and data analytics demands indicate that these tools 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 shortly discuss these trends and evaluate some current approaches to Big Data management and processing, identify the current challenges, and suggest possible research directions.