NGS Technologies have revolutionized genomic research with high-throughput, cost-effective sequencing technologies producing massive amounts of biological data. We discuss the interdependent development between NGS technologies and advanced big data analytics tools that has expedited discoveries across multiple domains such as precision medicine, cancer genomics, metagenomics, evolutionary biology, landscape genomics and a host of diverse applied applications. We discuss the computational hurdles associated with these large NGS datasets, and describe how state-of-the-art big data solutions, including cloud computing infrastructures, machine learning algorithms, and novel data visualization approaches are overcoming these challenges. The concurrent emergence of these two powerful technologies presents many opportunity, as demonstrated by case studies of breakthrough applications that drive discovery into critical biological systems. Lastly, we reflect on the lessons learnt, emerging trends and ethical considerations as well as future directions that will pave the way for the next phase of the genomic revolution. In this comprehensive review, we highlight how big data analytics opens new avenues in scientific discovery that have yet to be fully realized in the context of NGS technologies; reshaping both basic biological research and its subsequent clinical applications.