The computational models we will review here have attempted to account for subsets of the properties and paradigms used to study attention. In this chapter we will introduce the models and elaborate on the explanations they give to the diﬀerent aspects of attention. In the discussion section we will compare the diﬀerent models. It should be noted that our focus is on the major models used to simulate behavioural data. Hence, we exclude models which have primarily focused on applying the idea of selective attention to computer vision problems (e.g. Tsotsos et al., 1995) or on modelling the underlying neurobiology of attention (e.g. Braun, Koch, & Davis, 2001; Hamker, in press). We begin by considering models applied to two main paradigms used to study attention in humans-stimulus ﬁltering and visual search tasks. Typically, simulations of such tasks do not contain very elaborate mechanisms for object recognition. Models that incorporate procedures for object recognition as well as attention, then, provide a better account of the way in which object-and space-based selection interact and of how top-down knowledge can modulate bottom-up biases in selection. Consequently, we proceed to discuss these models before proceeding to outline how models can be applied to neuropsychological disorders such as visual agnosia and neglect.