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The reconstruction problems in optical and electrical tomography, such as Optical Diffusion Tomography and Electrical Impedance Tomography, are known to be severely ill-posed. In recent years several modalities have been introduced that circumvents the ill-posedness by introducing another physical modality. This leads to systems of coupled partial differential equations. By using the coupled-physics approach, reconstructions can then be computed with fine resolution and high contrast. To retrieve accurate information from the coupled data one solves the so-called quantitative reconstruction problem. In this mini-symposium we bring together experts working on different quantitative reconstruction problems with hybrid data and discuss future directions.