What do Toeplitz matrices, random matrix models, orthogonal polynomials, Painlevé transcendents, the KdV equation, and black holes, seemingly very unrelated subjects, have in common?  These, and a variety of other mathematical problems, can be studied by means of the so called Riemann-Hilbert method. In this talk we briefly describe what a Riemann-Hilbert problem is and present several recent applications, from the spectral properties of Toeplitz operators to exact solutions of Einstein's field equations.