<p>Numerous industrial, biological and geophysical fluids display the time-dependent rheological property known as thixotropy, in which the viscosity evolves over time and in response to changes in stress or strain rate. A wide range of phenomenological behaviour is associated with this property, and numerous models have been proposed and used to capture this. The aim of this paper is to classify systematically how modelling choices correspond to predicted behaviour, and, conversely, how observed behaviour can inform modelling choices. To this end, ‘ideal’ thixotropic models (without elasticity) are considered from a theoretical standpoint and the range of behaviour that different models can predict are explored. The approach is illustrated by considering the steady and transient responses to simple shear, with particular emphasis given to the role of the steady-state flow curve for a given model construction. The requirements for models to capture complex rheological phenomena like yield-stress ageing and “viscosity bifurcations” are outlined, and the implications of different modelling choices are discussed. The importance of carefully analysing the type of behaviour that a given thixotropic model can exhibit is highlighted.</p>