The Lewis-acid catalyzed rearrangement of parent trans-stilbene oxide 1 was studied with M(OTf)3/DCM and M(OTf)3/[BMIM][BF4] (M=Bi, Al, Ga, Sc, and Yb; [BMIM]=butylmethylimidazolium) and Zn(NTf2)2, and with Bi(OTf)3/[BMIM][X] (X=NTf2, OTf, PF6, and BF4), employing 5mol% of catalyst. Selective formation of 2,2-dipheylacetaldehyde 2 (phenyl migration product) was observed in all cases, with Bi(OTf)3 proving most efficient. The rearrangement of 1 was also effected in [BMIM][X] (X=NTf2, OTf, PF6, and BF4) without an added catalyst under microwave MW irradiation, and X=PF6 gave the highest yield and selectivity. Efficient and selective rearrangement of 1–2 was also observed with 0.1–0.3equiv. of [BMIM(SO3H)][OTf] in DCM and in [BMIM][X]. A substituent effect study was performed with a series of singly substituted 1,2-diphenyl oxiranes (with X=OMe, Me, F, CN, and NO2) with 5mol% Bi(OTf)3 in DCM and in [BMIM][NTf2]. Notable formation of ketones was observed with the NO2 and CN derivatives. Competing formation of ketones was also observed in [BMIM][PF6] under MW and under Brønsted acid catalysis with [BMIM(SO3H)][OTf] in DCM and in [BMIM][NTf2]. The aryl versus H migration was studied computationally by DFT and MP2 methods and by including solvation effects (IEFPCM).