Visual search, a vital task for humans and animals, has also become a common and important tool for studying many topics central to active vision and cognition ranging from spatial vision, attention, and oculomotor control to memory, decision making, and rewards. While visual search often seems effortless to humans, trying to recreate human visual search abilities in machines has represented an incredible challenge for computer scientists and engineers. What are the brain computations that ensure successful search? This review article draws on efforts from various subfields and discusses the mechanisms and strategies the brain uses to optimize visual search: the psychophysical evidence, their neural correlates, and if unknown, possible loci of the neural computations. Mechanisms and strategies include use of knowledge about the target, distractor, background statistical properties, location probabilities, contextual cues, scene context, rewards, target prevalence, and also the role of saliency, center-surround organization of search templates, and eye movement plans. I provide overviews of classic and contemporary theories of covert attention and eye movements during search explaining their differences and similarities. To allow the reader to anchor some of the laboratory findings to real-world tasks, the article includes interviews with three expert searchers: a radiologist, a fisherman, and a satellite image analyst.