In this talk I will introduce the idea of a Riemann-Hilbert problem. In a nutshell, this problem ask you to recover a complex function from its non-analytic behavior. We will derive a solution for a family of simple RH problems, and use some contour integral chicanery to solve a few examples. If time permits, I will describe how such problems are related to the inverse scattering transform used to solve nonlinear integrable PDEs.