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.