Vortex sheets are commonly used in fluid dynamics to represent thin shear layers in slightly viscous flow. Some of the first Lagrangian particle simulations in fluid dynamics used the point vortex approximation to study vortex sheet roll-up. I will review the early fundamental contributions on this topic by Rosenhead, Birkhoff, and Moore, and then discuss more recent developments concerning regularized point vortex simulations, spiral roll-up in the Kelvin-Helmholtz problem, and chaotic dynamics in vortex cores. Finally I will describe a new particle/panel method for vortex sheet roll-up in 3D flow which uses a treecode algorithm to advect the particles. Applications will be presented to vortex ring dynamics.