In this talk, we discuss a general framework that combines concepts from classical regularization theory with neural-network-based reconstruction methods. Particular emphasis is placed on the role of data consistency and the incorporation of problem-specific physical models into learning-based approaches. We introduce data-proximal null-space networks as a principled strategy for integrating learned image priors while maintaining consistency with the measured data. Furthermore, we present theoretical convergence results that extend existing regularization concepts to this setting. Numerical examples from limited-view computed tomography illustrate the practical performance and potential of the proposed framework.