Recent advances in experimental and computational methods are increasing the quantity and complexity of generated data. This massive amount of raw data needs to be stored and interpreted in order to advance the materials science field. Identifying correlations and patterns from large amounts of complex data is being performed by machine learning algorithms for decades. Recently, the materials science community started to invest in these methodologies to extract knowledge and insights from the accumulated data. This review follows a logical sequence starting from density functional theory as the representative instance of electronic structure methods, to the subsequent high-throughput approach, used to generate large amounts of data. Ultimately, data-driven strategies which include data mining, screening, and machine learning techniques, employ the data generated. We show how these approaches to modern computational materials science are being used to uncover complexities and design novel materials with enhanced properties. Finally, we point to the present research problems, challenges, and potential future perspectives of this new exciting field.