Abstract: When it comes to the question of what proofs serve for, since the antiquity two possible answers have been identified: on the one hand, a proof can serve to show that something is true, on the other hand, a proof can also serve to explain why something is true. The first type of proofs are called “proofs-that”, whilst the latter “proofs-why” or “explanatory proofs”. A great part of the logic of the XX century has been dedicated to the formalization and the development of proofs-that, leaving untouched the analysis of proofs-why. In this talk we will try to fill this gap and explore the realm of explanatory proofs. We will offer a formalization of explanatory proofs and we will attempt to show what type of results can be obtained with such a formalization.