Zr-based metal-organic frameworks (Zr-MOF) UiO-66 and UiO-67 catalyze thioether oxidation in nonprotic solvents with unprecedentedly high selectivity toward corresponding sulfones (96-99% at ca. 50% sulfide conversion with only 1 equiv of H2O2). The reaction mechanism has been investigated using test substrates, kinetic, adsorption, isotopic (O-18) labeling, and spectroscopic tools. The following facts point out a nucleophilic character of the peroxo species responsible for the superior formation of sulfones: (1) nucleophilic parameter X-Nu = 0.92 in the oxidation of thianthrene 5-oxide and its decrease upon addition of acid; (2) sulfone to sulfoxide ratio of 24 in the competitive oxidation of methyl phenyl sulfoxide and p-Br-methyl phenyl sulfide; (3) significantly lower initial rates of methyl phenyl sulfide oxidation relative to methyl phenyl sulfoxide (k(S)/k(SO) = 0.05); and (4) positive slope rho = +0.42 of the Hammett plot for competitive oxidation of p-substituted aryl methyl sulfoxides. Nucleophilic activation of H2O2 on Zr-MOF is also manifested by their capability of catalyzing epoxidation of electron-deficient C=C bonds in alpha,beta-unsaturated ketones accompanied by oxidation of acetonitrile solvent. Kinetic modeling on methyl phenyl sulfoxide oxidation coupled with adsorption studies supports a mechanism that involves the interaction of H2O2 with Zr sites with the formation of a nucleophilic oxidizing species and release of water followed by oxygen atom transfer from the nucleophilic oxidant to sulfoxide that competes with water for Zr sites. The nucleophilic peroxo species coexists with an electrophilic one, ZrOOH, capable of oxygen atom transfer to nucleophilic sulfides. The predominance of nucleophilic activation of H2O2 over electrophilic one is, most likely, ensured by the presence of weak basic sites in Zr-MOFs identified by FTIR spectroscopy of adsorbed CDCl3 and quantified by adsorption of isobutyric acid.