Consider looking at a bone scan or a CT to determine if a patient is responding to cancer treatment. Or, as a less life-and-death case, consider searching through a child's toy box for all the Lego pieces that can be used to build a roof on today's project. These are complex, extended visual searches for multiple instances of multiple target types, be they metastases of cancer or building blocks of a particular shape. How do humans perform such tasks and how can we help experts to perform more effectively the critical extended search tasks that our civilization has created in the clinic, the airport, and elsewhere? The past 25+ years have seen great progress in understanding the basic process of visual selective attention. That said, the bulk of the existing work involves brief episodes of search (seconds) for a single instance of a single class of target (e.g. find a red vertical line or this specific object). Typically, that target will be present on 50% or more of trials. In order to understand and improve upon socially important search tasks in radiology and elsewhere, we must investigate extended visual search tasks. The proposed work exploits three extended search paradigms, largely new to the study of human search. Foraging tasks are laboratory analogs of picking berries in a field or lung nodules in a chest CT. Observers try to select as many target items as possible in a fixed period of time. To model this behavior, the Guided Search (GS) model is augmented with ideas from the literature on animal foraging as well as decision theory and neuroeconomics. Hybrid Search tasks involve searching visual displays for any of several possible types of target (think of a shopping list or a checklist of signs of disease). These are combinations of visual search and memory search. It is possible to search for literally hundreds of distinct objects, held in memory. To model this behavior, ideas from the study of working memory and long-term memory (LTM) are brought into the GS framework. Finally, Hybrid Foraging tasks combine the demands of the foraging and hybrid tasks. Here, observers attempt to collect as many examples as possible of multiple types of targets. We use each of these methods in laboratory studies with non-expert observers and in experiments with expert radiologists. We seek to describe and model the fundamental processes of extended search and to improve the ability of radiologists and other experts to perform such searches. Of particular interest are searches for rare, low prevalence targets (e.g. cancer in a breast cancer screening population appears in about 0.3% of exams). False negative, miss errors are elevated at low prevalence in clinical settings. The proposed work suggests techniques for ameliorating this effect and examines the impact of prevalence in extended search tasks. In summary, this work develops an interdisciplinary extension of GS, applied to extended search tasks, with the ultimate goal of improving performance on the critical search tasks found in radiology and other socially important settings.