The talk will outline recent approaches for using (deep) convolutional neural networks to solve a wide range of inverse problems, such as image reconstruction in medical tomography. A key element is to use a neural network architecture for reconstruction that includes physics based models that describe how data is generated as well as its statistical properties Another is the possibility to integrate complex task related a priori information and elements of decision making into the reconstruction procedure. The resulting approach outperforms current state-of-the-art in terms of ‘quality’, computational speed and there is no need to manually set parameters as with variational methods. Furthermore, the amount of training data and network size can be kept surprisingly small. The talk will also touch upon further developments based on using generative adversarial networks for uncertainty quantification.