Abstract: Machine learning systems are not robust by default. Even systems that are reported to outperform humans in a particular domain can be shown to fail at solving problems with virtually small variations on the problem data. This talk will focus on robustness in supervised learning and representation learning. In particular, we will give an outline of the current work on robust training and verification, with an emphasis on the role played by optimization and model construction. Our goal will be to highlight the nature of the challenges that are faced in checking and ensuring that learning systems work according to desired specifications.