The stable isotopes of xenon, which have attracted interest for a number of reasons, span a transitional region that evolves from γ-soft structures for the lighter mass isotopes to nearly spherical 136Xe with a closed neutron shell. The nature of this transition, which is gradual, is not well understood. To provide detailed spectroscopic information on the Xe isotopes, we have studied 130,132,134,136Xe at the University of Kentucky Accelerator Laboratory using inelastic neutron scattering and γ-ray detection. These measurements yielded γ-ray angular distributions, branching ratios, multipole mixing ratios, and level lifetimes (from the Doppler-shift attenuation method), which allowed the determination of reduced transition probabilities and provided insight into the structure of these nuclei.