Motivated by the desire to understand the dynamics of light modes on various gravitational backgrounds, this talk summarizes recent results concerning properties of scalar, vector, and tensor excitations of black holes and integrable stringy geometries. For rotating black holes and for certain Wess-Zumino-Witten models, full separability of all dynamical equations is demonstrated, and symmetries underlying this property are uncovered. For other classes of integrable backgrounds, the energy spectra of various fields are evaluated, and the algebraic constructions of the corresponding eigenfunctions are presented. Join Zoom Meeting https://zoom.us/j/94137164225?pwd=ZTV3Z2c3aStOdk5sSFRRbkhQRUh5dz09 Meeting ID: 941 3716 4225 Passcode: 500873