RG functions are used in QFT to evolve theories between energy scales and are frequently used in both phenomenology and theory. Starting at the 3-loop order, certain RG functions start exhibiting poles in the dimensional expansion, contrasting with the expectation that they should be finite. In this talk, I will clarify how this issue can be understood and how it is linked with an ambiguity in choosing renormalization constants that goes beyond a simple choice of renormalization scheme. The discussion will lead to a preferred prescription for the RG functions, which guarantees finiteness.