  Metrics representing black holes in General Relativity may exhibit naked
singularities for certain values of their parameters. This is the case for
super-extremal ($J^2 > M>0$) Kerr and super-extremal ($|Q|>M>0$)
Reissner-N\"ordstrom spacetimes, and also for the negative mass Schwarzschild
spacetime. We review our recent work where we show that these nakedly singular
spacetimes are unstable under linear gravitational perturbations, a result that
supports the cosmic censorship conjecture, and also that the inner stationary
region beyond the inner horizon of a Kerr black hole ($J^2 <M$) is linearly
unstable.
