A powerful aspect of effective field theories is connecting scales through renormalisation group (RG) flow, encapsulated in the anomalous dimensions of the operators. The anomalous dimension matrix of the SMEFT encodes clues towards where to find relics of heavy new physics in data, but its unwieldy 2499x2499 size (at operator dimension six) makes it difficult to draw general conclusions. In this talk, I will review recent progress on understanding the structure of the matrix using on-shell methods. Pairing this with a flavour decomposition of the Wilson coefficient matrices, I will show that small subsystems emerge which mix almost exclusively amongst themselves. This deconstruction of the RGEs simplifies SMEFT phenomenology and provides a first step to understanding the IR-attractive directions in the SMEFT parameter space, hence closing in on natural places for heavy new physics to make itself known.