  We study CMV matrices by focusing on their right-limit sets. We prove a CMV
version of a recent result of Remling dealing with the implications of the
existence of absolutely continuous spectrum, and we study some of its
consequences. We further demonstrate the usefulness of right limits in the
study of weak asymptotic convergence of spectral measures and ratio asymptotics
for orthogonal polynomials by extending and refining earlier results of
Khrushchev. To demonstrate the analogy with the Jacobi case, we recover
corresponding previous results of Simon using the same approach.
