Deep Learning (DL) has become a pervasive approach in many machine learning tasks and in particular in image processing problems such as denoising, deblurring, inpainting and segmentation. The application of DL within inverse problems is less well explored because it is not trivial to include Physics based knowledge of the forward operator into what is usually a purely data-driven framework. In addition some inverse problems are at a scale much larger than image or video processing applications and may not have access to sufficiently large training sets. In this talk I will present some of our approaches for i) developing iterative algorithms combining data and knowledge driven methods with applications in medical image reconstruction ii) developing a learned PDE architecture for forward and inverse models of non-linear image flow. Joint work with : Marta Betcke, Andreas Hauptmann, Felix Lucka