This paper contains a critical review of available methodology for dealing with the motion of non-spherical particles at higher Reynolds numbers in the Eulerian-Lagrangian methodology for dispersed flow. First, an account of the various attempts to classify the various shapes and the efforts towards finding a universal shape parameter is given and the details regarding the significant secondary motion associated with non-spherical particles are outlined. Most investigations concerning large non-spherical particles to date have been focused on finding appropriate correlations of the drag coefficient for specific shapes either by parameter variation or by using shape parameters. Particular emphasis is here placed on showing the incapability of one-dimensional shape parameters to predict the multifaceted secondary motion associated with non-spherical particles. To properly predict secondary motion it is necessary to account for the non-coincidence between the center of pressure and center of gravity which is a direct consequence of the inertial pressure forces associated with particles at high Reynolds number flow. Extensions for non-spherical particles at higher Reynolds numbers are far in between and usually based on semi-heuristic approaches utilizing concepts from airfoil theory such as profile lift. Even for regular particles there seems to be a long way before a complete theory can be formulated. For irregular particles with small aspect ratio, where the secondary motion is insignificant compared to the effect of turbulence, the drag correlations based on one-dimensional shape parameters come to their right. The interactions between non-spherical particles and turbulence are not well understood and modeling attempts are limited to extending methods developed for spheres. (C) 2010 Elsevier B.V. All rights reserved.