Quantum calculations at the DFT-D3/def2-TZVPD level of theory have been used to examine complexes between O2YBr (Y.N, P, and As) molecules and several Lewis bases, that is, NH3, H2O, and HF. The interactions of the lone pair of the ammonia, water, and hydrogen fluoride with the sigma-hole and pi-hole of O2YBr molecules have been considered. In general, the complexes where the Lewis base lone pair interacts with the pi-hole are more favorable than those with sigma-hole. The nature of the interactions has been characterized with the Bader theory of atoms in molecules (MM). We have also studied the ability of trifluoronitromethane and nitromethane to interact with anions using their pi-hole along with an analysis the Cambridge Structural Database. We have found a large number of hits that provide strong experimental support for ability of the nitryl (-NO2) group to interact with anions and Lewis bases. In some X-ray structures, the pi-hole interaction is crucial in the crystal packing and has a strong influence in the solid state architecture of the complexes. Finally, due to the relevance in atmospheric chemistry, we have studied noncovalent sigma/pi-hole complexes of nitryl bromide with ozone.