Inverse problems in imaging range from tomographic reconstruction (CT, MRI, etc) to image deconvolution, segmentation, and classification, just to name a few. In this talk I will discuss approaches to inverse imaging problems which have both a mathematical modelling (knowledge driven) and a machine learning (data-driven) component. Mathematical modelling is crucial in the presence of ill-posedness, making use of information about the imaging data, for narrowing down the search space. Such an approach results in highly generalizable reconstruction and analysis methods which come with desirable solutions guarantees. Machine learning on the other hand is a powerful tool for customising methods to individual data sets. Highly parametrised models such as deep neural networks in particular, are powerful tools for accurately modelling prior information about solutions. The combination of these two paradigms, getting the best from both of these worlds, is the topic of this talk, furnished with examples for image classification under minimal supervision and for tomographic image reconstruction.