Recently developed models, describing the disintegration of liquid jets and the dynamics of vortex ring-like structures at Diesel and gasoline engine-like conditions, are reviewed. The results of comparative analysis of modal and non-modal hydrody-namic instabilities of round viscous fluid jets are presented. Analytical formulae for vortex ring translational velocities, predicted by vortex ring models, are compared with the results of numerical solutions to the underlying equations and experimental data. A new approach to numerical simulation of two-phase two-dimensional flows, based on a combination of the full La-grangian method for the dispersed phase and the vortex blob method for the carrier phase, is discussed. © 2013 The Authors.