In two experiments we investigated the relationship between eye movements and performance in visual search tasks of varying difficulty. Experiment 1 provided evidence that a single process is used for search among static and moving items. Moreover, we estimated the functional visual field (FVF) from the gaze coordinates and found that its size during visual search shrinks with increasing task difficulty. In Experiment 2, we used a gaze-contingent window and confirmed the validity of the size estimates. The experiment also revealed that breakdown in robustness against item motion is related to item-by-item search, rather than search difficulty per se. We argue that visual search is an eye-movement-based process that works on a continuum, from almost parallel (where many items can be processed within a fixation) to completely serial (where only one item can be processed within a fixation). (Contains 15 figures.)