IEM laboratories have addressed the fundamental challenge of massive data availability to learning algorithms, which is captured by the following computational dogma: Running time of a learning algorithm increases with the size of the data. However, IEM laboratories’ recent research has shown that this dogma is false in general, and supports an emerging perspective in computation: Data should be treated as a resource that can be traded off with other resources, such as running time. We confront such emerging data science challenges in a unified mathematical framework by developing groundbreaking new optimization theory and methods for large-scale problems, characterizing the time and data required to reach approximate solutions along with their statistical guarantees. In addition, at IEM new learning approaches for signal and image processing representations have been developed, which enable the description of relevant information in data with sparse sets of of discriminative features. Significant methodological advances, strong theoretical results and novel applications have been developed in the area of signal, image, video and 3D data processing, analysis and coding. Similarly, IEM labs have been among the world pioneers to develop work in graph signal processing with the objective of analyzing data living on networks or irregular structures, with numerous applications in machine learning and data mining. Brain networks analysis has also been largely investigated in IEM, as well as several challenging applications in medical image analysis, or computer vision in general. This key research path has led to important breakthroughs in the understanding of the brain, or the heart characterization. Finally, important technological advances have been taking place in IEM in the domain of image and visual information compression, where EPFL has been recognized as a world leader for several years.