Do mathematical diagrams used in science have a function that goes beyond that of representing the phenomena and stretches to that of ‘explaining’ them? According to some philosophers of mathematics, mathematical diagrams may have such an ‘explanatory’ function. Moreover, other scholars consider that visual reasoning on diagrams can form a non-superfluous part of a process of explaining a scientific fact. Nevertheless, these claims lack sufficient justification and there is no trace in the literature of a single paper or research project explicitly devoted to the explanatory role of visual reasoning and mathematical diagrams in mathematical and scientific explanation. The connection between visual reasoning and mathematical explanation, and more generally the role of mathematical diagrams in scientific practice, remains an extensive and still largely unexplored terrain, potentially fruitful for the philosophy of mathematics and the general philosophy of science. The main aim of the present research project is to fill this gap and offer an extensive and detailed philosophical analysis of the representational and explanatory role of diagrams and visual reasoning in scientific and mathematical explanation. In particular, through the refinement of my account of mathematical explanation, or the elaboration of a new philosophical framework, the goal of this project is to unveil whether, how and when visual reasoning and mathematical diagrams have explanatory power when used to study and represent a physical phenomenon.