I will discuss classes of hidden symmetries of gravity and their consequences for black holes and compact objects. 
It is well known that asymptotically flat black holes in general relativity have a vanishing static tidal response (i.e., zero Love numbers). In the talk, I will first show that this is the result of a hidden structure of ladder symmetries governing static (spin 0,1,2) perturbations around black holes, and I will discuss the underlying geometric origin. I will also present examples of hidden symmetries and dualities at finite frequency and their consequences for quasinormal modes. I will finally briefly present an effective field theory for perturbations around black holes in scalar-tensor theories and discuss how to connect the effective couplings to possible deviations in the observed ringdown frequencies.