Pulmonary emphysema is characterized by irreversible destruction of lung parenchyma. Emphysema is a major contributor to chronic obstructive pulmonary disease (COPD), which by itself is a major cause of morbidity and mortality in the western world. Computed tomography (CT) is an established method for the in-vivo analysis of emphysema. This review first details the pathological basis of emphysema and shows how the subtypes of emphysema can be characterized by CT. The review then shows how CT is used to quantify emphysema, and describes the requirements and foundations for quantification to be accurate. Finally, the review discusses new challenges and their potential solution, notably focused on multi-detector-row CT, and emphasizes the open questions that future research on CT of pulmonary emphysema will have to address.