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Current computed tomography (CT) technology allows for near isotropic, submillimeter resolution acquisition of the complete chest in a single breath hold. These thin-slice chest scans have become indispensable in thoracic radiology, but have also substantially increased the data load for radiologists. Automating the analysis of such data is, therefore, a necessity and this has created a rapidly developing research area in medical imaging. This paper presents a review of the literature on computer analysis of the lungs in CT scans and addresses segmentation of various pulmonary structures, registration of chest scans, and applications aimed at detection, classification and quantification of chest abnormalities. In addition, research trends and challenges are identified and directions for future research are discussed.