We present a review of results on asymptotics of orthogonal
polynomials, stressing their spectral aspects and similarity in two cases
considered. They are polynomials orthonormal on a finite union of disjoint
intervals with respect to the Szegö weight and polynomials orthonormal
on the whole line with respect to varying weights and having
the same union of intervals as the set of oscillations of asymptotics. In
both cases we construct double infinite Jacobi matrices with generically
quasiperiodic coefficients and show that each of them is an isospectral
deformation of another. Related results on asymptotic eigenvalue
distribution of a class of random matrices of large size are also
discussed.