Abstract: We employ the theory of orthogonal polynomials on the unit circle to compute the eigenvalue distribution of truncated unitary random matrices (with one row and column removed). These appear as scattering resonances of open quantum systems. We also show that zeros of orthogonal polynomials with decaying random Verblunsky coefficients asymptotically behave like these eigenvalues. Finally, we will briefly discuss the distribution of the resonances of Hermitian random matrices coupled to the discrete Laplacian on the lattice $Z_+$. We reduce this problem to the resonance problem for Jacobi operators and use the theory of orthogonal polynomials on the real line. Joint work with Rowan Killip.