  We describe an approach to universality limits for orthogonal polynomials on
the real line which is completely local and uses only the boundary behavior of
the Weyl m-function at the point. We show that bulk universality of the
Christoffel-Darboux kernel holds for any point where the imaginary part of the
m-function has a positive finite nontangential limit. This approach is based on
studying a matrix version of the Christoffel-Darboux kernel and the realization
that bulk universality for this kernel at a point is equivalent to the fact
that the corresponding m-function has normal limits at the same point. Our
approach automatically applies to other self-adjoint systems with $2\times 2$
transfer matrices such as continuum Schr\"odinger and Dirac operators. We also
obtain analogous results for orthogonal polynomials on the unit circle.
