A number of today's accepted basic viewpoints related to cationic ring-opening polymerizations (CROP) were a matter of vivid disagreements between various research groups in the past. These controversies are described in this article and reasons of some differencies in opinions are explained. It is shown in which way we learned that polyacetals are not exclusively cyclic (as it was assumed), why CROP ions and ion pairs have similar reactivities, and why it was necessary to propose that CROP proceeds at certain conditions by Activated Monomer Mechanism. Among other subtle kinetic problems, application of the dynamic NMR and "temperature jump" techniques in determining rate constants of active species interconversions are discussed.