  We prove the edge universality of the beta ensembles for any $\beta\ge 1$,
provided that the limiting spectrum is supported on a single interval, and the
external potential is $\mathscr{C}^4$ and regular. We also prove that the edge
universality holds for generalized Wigner matrices for all symmetry classes.
Moreover, our results allow us to extend bulk universality for beta ensembles
from analytic potentials to potentials in class $\mathscr{C}^4$.
