  This paper provides an overview of current approaches for solving inverse
problems in imaging using variational methods and machine learning. A special
focus lies on point estimators and their robustness against adversarial
perturbations. In this context results of numerical experiments for a
one-dimensional toy problem are provided, showing the robustness of different
approaches and empirically verifying theoretical guarantees. Another focus of
this review is the exploration of the subspace of data-consistent solutions
through explicit guidance to satisfy specific semantic or textural properties.
