Investigations were made of rotary resonance recouplings (R-3) of chemical shift anisotropy (CSA), heteronuclear dipolar (HTD), and homonuclear dipolar (HMD) couplings involving half-integer quadrupolar nuclei under magic-angle sample spinning condition. Under rotary resonance conditions provided by a low amplitude rf field and a high spinning speed, the spectrum of the central transition coherence of half-integer quadrupolar nuclei shows recouplings of CSA, HTD, and HMD interactions that depend on the ratio of the rf field to the spinning speed. These new properties can be used to extract electronic and structural information about the sample that are otherwise difficult to extract in the presence of a dominant quadrupolar interaction. An average Hamiltonian theory is used to explain the recoupling properties of various interactions. Experimental implementations of the R-3 are demonstrated on model compounds with spin-3/2 systems.