Herein, we review aspects of leading-edge research and innovation in materials science that exploit big data and machine learning (ML), two computer science concepts that combine to yield computational intelligence. ML can accelerate the solution of intricate chemical problems and even solve problems that otherwise would not be tractable. However, the potential benefits of ML come at the cost of big data production; that is, the algorithms demand large volumes of data of various natures and from different sources, from material properties to sensor data. In the survey, we propose a roadmap for future developments with emphasis on computer-aided discovery of new materials and analysis of chemical sensing compounds, both prominent research fields for ML in the context of materials science. In addition to providing an overview of recent advances, we elaborate upon the conceptual and practical limitations of big data and ML applied to materials science, outlining processes, discussing pitfalls, and reviewing cases of success and failure.