One of the most characteristic features of turbulence in three-dimensional incompressible fluids is enhanced energy dissipation. Most attempts to explain this phenomenon appeal to the remarkable Lagrangian properties of vorticity for inviscid flows. I review some of the ideas that have been proposed, including vortex stretching, vortex reconnection and cross-stream vortex transport, especially in light of recent work which suggests non-uniqueness of Lagrangian trajectories in the limit of zero viscosity.