Computed tomography (CT) is the modality of choice for imaging the lungs in vivo. Sub-millimeter isotropic images of the lungs can be obtained within seconds, allowing the detection of small lesions and detailed analysis of disease processes. The high resolution of thoracic CT and the high prevalence of lung diseases require a high degree of automation in the analysis pipeline. The automated segmentation of pulmonary structures in thoracic CT has been an important research topic for over a decade now. This systematic review provides an overview of current literature. We discuss segmentation methods for the lungs, the pulmonary vasculature, the airways, including airway tree construction and airway wall segmentation, the fissures, the lobes and the pulmonary segments. For each topic, the current state of the art is summarized, and topics for future research are identified.