Fluorescence microscopy imaging involves a wide range of inverse problems in which it is necessary to reconstruct meaningful representations of biological samples from incomplete and noisy measurements. These problems are inherently ill-posed and lead to solutions that are highly sensitive to small perturbations. Existing model-based approaches rely on expert knowledge of the underlying reconstruction procedures to ensure stability, as well as on ad hoc optimisation methods, which limits their practical applicability. The MALIN project, funded by the ERC, addresses these limitations by developing an integrative framework that combines model-based methods with data-driven deep learning techniques. From a methodological perspective, the project focuses on optimisation-oriented approaches that incorporate available physical knowledge and account for modelling uncertainties. The resulting methods improve efficiency, accuracy and cost-effectiveness and are disseminated via open-source software tools.