  We discuss conceptual aspects of renormalization in the context of effective
field theories for the two-nucleon system. It is shown that, contrary to
widespread belief, renormalization scheme dependence of the scattering
amplitude can only be eliminated up to the order the calculations are
performed. We further consider an effective theory for an exactly solvable
quantum mechanical model which possesses a long- and short-range interaction to
simulate pionful effective field theory. We discuss the meaning of low-energy
theorems in this model and demonstrate their validity in calculations with a
finite cutoff $\Lambda$ as long as it is chosen of the order of the hard scale
in the problem. Removing the cutoff by taking the limit $\Lambda \to \infty$
yields a finite result for the scattering amplitude but violates the low-energy
theorems and is, therefore, not compatible with the effective field theory
framework.
