For technological design and operation of hydrocyclone classification a separation model should be available, which largely comprises the physical phenomena of the process, reflects their effects by appropriate process parameters and can be mathematically formulated as separation function. The most models, which are known so far, do not meet these requirements in their entirety. In the main they have been empirically formulated and/or do not reflect that the separation effect, caused by the centrifugal field, is superimposed by an intensive mixing effect caused by the macroturbulence of the hydrocyclone flow. Only the models of turbulent cross-flow classification, which are adjusted to the conditions of hydrocyclone classification in dilute suspensions, come in the form of the tapping model or partition model close to the satisfaction of the demands mentioned above. After outlines of the characteristics and the transport phenomena of turbulent flows as well as of the indispensable simplifications and adjustments to given materials, geometrical and hydrodynamical properties, the model derivation is described. In particular the wide range of the rheological properties of the feed suspensions as well as the phenomena of turbulence damping cause restrictions regarding the quantification of the model predictions. Further improvements of the model predictions are only attainable by means of empirical adjustment corrections. In order to ensure an adequate reliability of the correction factors, they should be determined using similar material systems and also similar hydrocyclones. Meanwhile several working teams have successfully tested the efficiency of such models for dilute flow classification. The first and so far only known model development for dense flow classification in hydrocyclones starts from the fact that the operation space must be divided into two subspaces and thus also two subprocesses, namely the sediment formation in the outer subspace and the formation of the radial concentration profiles of the particle sizes in the inner suspension subspace. Progress in this field necessitates further research. The so-called fishhook effect is based on flow forces, which cause an enrichment of finest particles in the zones of the velocity gradients around settling coarser particles in a certain Re-range, and superimposes the turbulent cross-flow classification. (C) 2010 Elsevier B.V. All rights reserved.