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Modern models of flow and transport across environmental and industrial porous media have reached a remarkable level of complexity, with the aim of capturing the nature of target phenomena and processes. The level of complexity of these models could hamper unambiguous understanding of relationships among model inputs and outputs of interest. This is a critical aspect in a variety of scenarios, including flow and reactive transport in heterogenous aquifers and sustainable use of underground resources. All of these settings are associated with multiple sources of uncertainty. These are typically linked to (i) our conceptual understanding of how a natural system functions and the possibility of depicting its key features through various modeling approaches/formulations, (ii) our knowledge of model parameters and/or initial and boundary conditions, and (iii) the amount of available data/information and the scale with which these are associated. In this broad context, emphasis is here devoted to model diagnosis through (moment- and distribution- based) local and global sensitivity analyses embedding model, process, and parameter uncertainty. Exemplary applications encompass a variety of scales (from pore- to field-scale) and processes, including reactive chemical transport and contaminants of emerging concern.