The literature on thixotropy modeling is reviewed, with particular emphasis on models for yield stress materials that possess elasticity. The various possible approaches that have been adopted to model the different facets of the mechanical behavior of this kind of materials are compared and discussed in detail. An appraisal is given of the advantages and disadvantages of algebraic versus differential stress equations. The thixotropy phenomenon is described as a dynamical system whose equilibrium locus is the flow curve, and the importance of using the flow curve as an input of the model is emphasized. Different forms for the evolution equation for the structure parameter are analyzed, and appropriate choices are indicated to ensure a truthful description of the thixotropy phenomenon. (C) 2012 Elsevier B.V. All rights reserved.