The talk presents recent advances at the intersection of computational imaging and machine learning, illustrating how physical models and data-driven approaches can be combined to address complex inverse problems. Through applications in biomedical imaging, microscopy, and cultural heritage reconstruction, we will show how computational mathematics contributes to building reliable, interpretable, and efficient learning-based methods. Emphasis will be placed on model-based regularization, optimization techniques, and physics-informed learning as key tools for designing robust and principled imaging algorithms.