The main ideas of simulation of two-phase flows, based on a combination of the conventional Lagrangian or fully Lagrangian (Osiptsov) approaches for the dispersed phase and the mesh-free vortex and thermal-blob methods for the carrier phase, are summarised. In the approach based on a combination of the fully Lagrangian approach for the dispersed phase and the vortex blob methods for the carrier phase the problem of calculation of all parameters in both phases (including particle concentration) is reduced to the solution of a high-order system of ordinary differential equations, describing transient processes in both carrier and dispersed phases. It contrast to this approach, in the approach based on a combination of the conventional Lagrangian approaches for the dispersed phase and the vortex and thermal-blob methods for the carrier phase the non-isothermal effects in the two-phase flow were taken into account. The one-way coupled, two-fluid approach was used in the analysis. The gas velocity field was restored using the Biot-Savart integral. Both these approaches were applied to modelling of two processes: the time evolution of a two-phase Lamb vortex and the development of an impulse two-phase jet. Various flow patterns were obtained in the calculations, depending on the initial droplet size.