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In this talk I will present our past and recent activities for learning better variational models for inverse problems in imaging. Starting from first-principles based models such as the total variation, I show the evolution of our work to more complicated models based on higher-order derivatives or curvature to fully learned models. Applying an optimal-control based early stopping strategy to the learned models yields "Variational Networks" that can be interpreted as a particular form of recurrent convolutional neural network. In order to visualize and better understand their properties, we use a non-linear eigenmode analysis that reveals interesting properties of the learned models. I will demonstrate the excellent performance of our models through various inverse imaging problems ranging from simple image restoration to medical image reconstruction. Thomas Pock Graz University of Technology, Austria