In this talk, we give an overview on different imaging problems, that inherently suffer from instabilities. The first topic we present is region-of-interest computerized tomography. This problem can be related to the inversion of a truncated Hilbert transform and suffers from severe ill-posedness. We provide a thorough spectral analysis of this operator and show how this knowledge can be employed to derive regularization results. Next, we present phase retrieval, a problem that arises in coherent diffraction imaging (CDI), a nanoscale lensless imaging technique. Due to the nature of the data acquisition, the measurements do not contain phase information. Motivated by a technique known as ptychography in CDI, we analyze phase retrieval in the setting where the measurement system is a frame, i.e. carries some redundancy. In the final part, we turn to image classification and image reconstruction through deep neural networks (DNNs). While this modern technique has enjoyed increasing popularity in recent years, we highlight stability issues in DNNs, also known as adversarial attacks. We present an algorithm of constructing a new type of attack through small imperceptible deformations of the input.