Modern deep generative models like GANs, VAEs and invertible flows are showing amazing results on modeling high-dimensional distributions, especially for images. We will show how they can be used to solve inverse problems by generalizing compressed sensing beyond sparsity, extending the theory of Restricted Isometries to sets created by generative models. We will present the general framework, new results and open problems in this space. Bio: Alex Dimakis is an Associate Professor at the Electrical and Computer Engineering department, University of Texas at Austin. He received his Ph.D. from UC Berkeley and the Diploma degree from the National Technical University of Athens. His research interests include information theory, coding theory and machine learning.