During language comprehension, information about the world is exchanged and processed. Two essential ingredients of everyday cognition that are employed during language comprehension are the ability to reason counterfactually, and the ability to understand and predict other peoples' behaviour by attributing independent mental states to them (theory of mind). We report two visual-world studies investigating the extent to which the constraints of world knowledge and prior context, as established by a counterfactual (Exp. 1) or a false belief situation (Exp. 2), influence eye-movements directed towards objects in a visual field. Proportions of anticipatory eye-movements indicated an initial visual bias towards "contextually supported" referents in both studies. Thus, we propose that when visual information is available to reinforce linguistic input, participants "expect" a context-relevant continuation. Shortly after the critical word onset, the "linguistically supported" referent was visually favoured, with counterfactual (but not false belief) contexts revealing a temporal delay in integrating factually inconsistent language input. Results are discussed in relation to accounts of discourse processing and the processing relationship between counterfactual and theory of mind reasoning. Finally, we compare findings across different experimental paradigms and propose a novel cluster-analytic procedure to identify time-windows of interest in visual-world data. (Contains 11 footnotes, 8 tables, and 11 figures.)