Various existing analytical descriptions for predicting turbulent flows laden with solid particles or liquid droplets are reviewed here. The main focus is on a collisionless dispersed phase, however, the two-way coupling effects are considered and discussed. The review of various methods is conducted by dividing them into two main categories. The first category includes direct numerical simulation (DNS), large-eddy simulation, and stochastic modelling, which are collectively called the 'Lagrangian description'. The second category, under the 'Eulerian description', includes Reynolds averaged Navier-Stokes (RANS) and probability density function (pdf) modelling. The emphasis is placed on application of these approaches for both understanding and prediction of turbulent dispersed phase. The discussion is focused on merits and limitations of these approaches and the nature of predictions offered by them. The mathematical aspects of RANS and pdf modelling are presented in greater detail. The important role of DNS generated data in the development and assessment of other approaches is discussed with the aid of some representative examples in particle-laden homogeneous turbulent flows. (C) 2003 Elsevier Ltd. All rights reserved.