Orthogonal polynomials with inserted point masses

Let $d\mu$ be a probability measure on the unit circle. We add a pure point $\zeta\in\partial\mathbb D$ to $d\mu$ to form the probability measure $d\nu$. We will discuss some new results concerning this point mass perturbation, including its effects on the Verblunsky coeffcients of $d\nu$, as well as the asymptotics of orthogonal polynomials of $d\nu$.