A meromorphic inner function is a bounded analytic function on the upper half plane with unit modulus almost everywhere on the real line and a meromorphic continuation to the complex plane. Meromorphic inner functions appear in spectral theory of differential operators, Krein-de Branges theory of entire functions, and the study of Toeplitz operators and nonlinear Fourier transform. In this talk I will discuss some uniqueness problems for meromorphic inner functions and their applications to spectral theory of differential operators.