This paper provides a multi-disciplinary overview of the research issues and achievements in the field of Big Data and its visualization techniques and tools. The main aim is to summarize challenges in visualization methods for existing Big Data, as well as to offer novel solutions for issues related to the current state of Big Data Visualization. This paper provides a classification of existing data types, analytical methods, visualization techniques and tools, with a particular emphasis placed on surveying the evolution of visualization methodology over the past years. Based on the results, we reveal disadvantages of existing visualization methods. Despite the technological development of the modern world, human involvement (interaction), judgment and logical thinking are necessary while working with Big Data. Therefore, the role of human perceptional limitations involving large amounts of information is evaluated. Based on the results, a non-traditional approach is proposed: we discuss how the capabilities of Augmented Reality and Virtual Reality could be applied to the field of Big Data Visualization. We discuss the promising utility of Mixed Reality technology integration with applications in Big Data Visualization. Placing the most essential data in the central area of the human visual field in Mixed Reality would allow one to obtain the presented information in a short period of time without significant data losses due to human perceptual issues. Furthermore, we discuss the impacts of new technologies, such as Virtual Reality displays and Augmented Reality helmets on the Big Data visualization as well as to the classification of the main challenges of integrating the technology.