  Low-energy effective theories have been used very successfully to study the
low-energy limit of QCD, providing us with results for a plethora of phenomena,
ranging from bound-state formation to phase transitions in QCD. These theories
are consistent quantum field theories by themselves and can be embedded in QCD,
but typically have a physical ultraviolet cutoff that restricts their range of
validity. Here, we provide a discussion of the concept of renormalization group
consistency, aiming at an analysis of cutoff effects and regularization-scheme
dependences in general studies of low-energy effective theories. For
illustration, our findings are applied to low-energy effective models of QCD in
different approximations including the mean-field approximation. More
specifically, we consider hot and dense as well as finite systems and
demonstrate that violations of renormalization group consistency affect
significantly the predictive power of the corresponding model calculations.
