Prompt and delayed gamma-ray cascades in doubly magic 132Sn and its neighbor 131Sn have been studied at Gammasphere using a 248Cm fission source. Isotopic assignments of unknown gamma rays were based on coincidences with known transitions in A = 112-116 Pd fission partners. The yrast level spectra of both tin nuclei are interpreted using empirical nucleon-nucleon interactions from the 132Sn and 208Pb regions. Results include identification of the (nuf(7/2)h(-1)(11/2))9(+) aligned state in 132Sn and of extensive (nuf(7/2)h(-2)(11/2)), (nuf(7/2)d(-1)(3/2)h(-1)(11/2)) and (nuh(-1)(11/2)x3(-)) multiplets in 131Sn. The previously reported beta(-) decay of an unusual 131In high-spin isomer to levels in 131Sn is also elucidated.