Renormalization group methods: Which kind of explanation?

Renormalization and Renormalization Group (RG) have proven to be very powerful tools in contemporary physics, with a decisive influence on how to conceive of key physical aspects, including theories themselves. While they can be tackled from a variety of standpoints, this paper focuses on a specific philosophical issue, that is, which kind of explanation can be provided by means of RG methods. After a short, historical overview to set out the physical context, we scrutinize recent debates on the topic, with a particular focus on Morrison's seminal work. With respect to her account, where RG explanation is portrayed as mathematical, non-reductive, and non-causal, our focus is on the first aspect. Our claim is that RG theory's explanatory role cannot reside exclusively in its mathematical character, independently from a physical interpretation: mathematical and physical features intersect in a highly non-trivial way to provide an explanation of physical phenomena.