The basic principles of theLagrangian-Eulerian Eulerian-Eulerian-EulerianEulerian and Lagrangian-Eulerian approaches to modelling multiphase flowsSprays (sprays) are described. The details of the analytical solution to the equation for droplet velocityDroplet velocity in a viscous flowViscous flow, leading to the concept of velocity relaxationVelocity relaxation, are presented. Stability analysisStability analysis of a plane inviscid flowInviscid flow with density and velocity jump is detailed. This analysis leads to a dispersion equationDispersion equation based on which the stability or instabilityInstability of the flow is established. TheRayleigh-Taylor Rayleigh-Taylor and Kelvin-HelmholtzKelvin-Helmholtz flow instabilities are identified using this equation. The key assumptions of the classical WAVE modelWAVE model for jet breakup are described. These include the assumption that the velocity inside the round jet is constant, and that of the inviscid ambient gasAmbient gas is zero. The formulae for the maximal growth rateGrowth rate of the instabilityInstability of this jet and the corresponding wavelengthWavelength are presented. These formulae are simplified at the limits of small and large Weber numbersWeber number. The time evolution of the average droplet radius during the development of the instabilityInstability is approximated by the rate equationRate equation. The criteria for bagBag and strippingStripping breakups of droplets and characteristic relaxation timesRelaxation time for them are shown. Further developments of the WAVE modelWAVE model are described.