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This talk will focus on beyond the standard model physics that can be probed in neutrino oscillations. When the dynamics of neutrino mass generation occurs around the TeV scale, sizable nonstandard neutrino interactions (NSI) may arise, which will be discussed. One focus of the talk is the Zee model of neutrino mass, where these NSIs can lead to observable signatures. I will also describe new ways of testing this scenario in IceCube by the observation of scalar resonances (termed Zee burst), similar to the Glashow resonance. Finally, I shall elaborate on theories of Dirac neutrino masses, which can arise naturally in certain left-right gauge models.