I will discuss a class of Riemann-Hilbert problems which arise naturally in Donaldson-Thomas theory. They involve maps from the complex plane to an algebraic torus which have prescribed discontinuities along a given collection of rays, and are closely related to the problems considered by Gaiotto, Moore and Neitzke. I will explain that in the `uncoupled' case these Riemann-Hilbert problems have unique solutions which can be written explicitly as products of gamma functions. If there's time I'll also discuss the case of the resolved conifold, where the Riemann-Hilbert problem leads naturally to the string partition function.