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.