This MSc lecture at TU Darmstadt begins by covering basic concepts of robust statistics and data science. Then we move on to supervised and unsupervised learning problems and describe current robust data science methods (e.g., in regression and classification, cluster analysis) before treating the challenging high-dimensional setting, where structural assumptions, such as sparsity are needed to find a solution. Biomedical applications including health monitoring using wearable devices, and genomic data analysis are discussed. Open-source toolboxes are provided, enabling students to try out the methods that are discussed in the lecture.