The experimental rate law for the Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) reaction was found to vary in complex ways with concentration, the presence of chloride ion, and the presence of accelerating ligands. Several examples of discontinuous ("threshold behavior") kinetics were observed, along with a decidedly nonlinear correlation of electronic substituent parameter with the rate of CuAAC reaction with p-substituted arylazides. The previously observed tendency of the CuAAC reaction to provide ditriazoles from a conformationally constrained 1,3-diazide was found to be affected by a class of polybenzimidazole ligands introduced in the accompanying article. Various lines of evidence suggest that the standard tris(triazolylmethyl)amine ligand binds less strongly to Cu(I) than its benzimidazole analogues. On the basis of these observations, it is proposed that (a) a central nitrogen donor provides electron density at Cu(I) that assists the cycloaddition reaction, (b) the three-armed motif bearing relatively weakly coordinating heterocyclic ligands serves to bind the metal with sufficient strength while providing access to necessary coordination site(s), (c) at least two active catalysts or mechanisms are operative under the conditions studied, and (d) pendant acid or ester arms in the proper position can assist the reaction by speeding the protiolysis step that cleaves the Cu-C bond of a Cu.triazolyl intermediate.