WHY 2 RENORMALIZATION-GROUPS ARE BETTER THAN ONE

The advantages of using more than one renormalization group (RG) in pr oblems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary informat ion, i.e. what is very difficult to calculate with an RG based on one flow parameter may be much more accesible using another; ii) using mor e than one RG requires less physical input in order to describe via RG methods the theory as a function of its parameters; iii) using more t han one RG allows one to describe problems with more than one divergin g length scale. The above points are illustrated concretely in the con text of both particle physics and statistical physics using the techni ques of environmentally friendly renormalization. Specifically, finite temperature lambda psi(4) theory, an Ising-type system in a film geom etry, an Ising-type system in a transverse magnetic field, the QCD cou pling constant at finite temperature and the crossover between bulk an d surface critical behavior in a semi-infinite system are considered.