Excited states of the rubidium isotopes 3787, 89, 91Rb have been studied at the INFN Legnaro National Laboratory. Measurements of the γγ-ray decay of fragments produced in binary grazing reactions resulting from the interaction of a beam of 530 MeV 96Zr ions with a 124Sn target have been complemented by studies of the γγ-ray decay of fission fragments produced in the interaction of a beam of 230 MeV 36S ions with a thick 176Yb target. The structure of the yrast states of 3787, 89, 91Rb has been discussed within the context of spherical shell-model and cranked Nilsson-Strutinsky calculations.