When is field theory effective?

We analyze the relation between quark and hadron degrees of freedom in QCD in 3+1 and in 1+1 dimensions. In both cases in the weak-confinement limit low-energy properties such as charge radii of mesons are poorly described by effective field theory, yet easily calculable in terms of quarks wave functions. Effective field theory fails because higher-dimensions operators acquire anomalously large coefficients. In 1+1 dimensions, the theory is solved for strong confinement as well, working in the large-Nc limit. For strong coupling we find that effective field theory emerges as a powerful tool and there are indications that the quark model remains useful too. We characterize the relation between the quark and hadron expansions, and obtain insight into when and why effective field theories are valid. (orig.)