Gustavsson proved that the fluctuations of a bulk GUE eigenvalue around its mean are asymptotically Gaussian after a suitable rescaling. O'Rourke extended this to the GOE and GSE using a coupling of Forrester and Rains. In this talk we present recent results on the universality of these fluctuations for other classes of random matrices, including matrices of general Wigner-type under a one-cut...