This chapter provides a critical survey of the use of vorticity elements for simulation of vortex flows. The traditional singular vortex and vortex blob methods are described for inviscid two-dimensional vortex flows. The necessity of the regridding procedure for accurate solution of the vorticity transport equation is discussed. A vorticity collocation approach is introduced, which directly solves the vorticity transport equation on the Lagrangian elements without the need for regridding. Extension of these methods to three-dimensional vortex transport is examined, including introduction of the fast multipole method for accelerated velocity computation. Application of vortex elements for simulation of vortex filament motion is examined, along with a spectral filter for regularization of a numerical instability on the filament motion. Five different methods for accounting for viscous diffusion on the Lagrangian vorticity elements are examined. Issues with prescribing vorticity boundary conditions to satisfy the no-slip condition on a body in a viscous flow are discussed. Finally, we examine use of discrete Burger’s vortex elements as a method of modeling coherent vortex effects in turbulence and for generation of synthetic turbulence.