Chest CT is often used for localizing and quantitating pathologies associated with chronic obstructive pulmonary disease (COPD). While simple measurements of areas and volumes of emphysema and airway structure are common, these methods do not capture the structural complexity of the COPD lung. Since the concept of fractals has been successfully applied to evaluate complexity of the lung, this review is aimed at describing the fractal properties of airway disease, emphysema, and vascular abnormalities in COPD. An object forms a fractal if it exhibits the property of self-similarity at different length scales of evaluations. This fractal property is governed by power-law functions characterized by the fractal dimension (FD). Power-laws can also manifest in other statistical descriptors of structure such as the size distribution of emphysema clusters characterized by the power-law exponent D. Although D is not the same as FD of emphysematous clusters, it is a useful index to characterize the spatial pattern of disease progression and predict clinical outcomes in patients with COPD. The FD of the airway tree shape and the D of the size distribution of airway branches have been proposed indexes of structural assessment and clinical predictions. Simulations are also useful to understand the mechanism of disease progression. Therefore, the power-law and fractal analysis of the parenchyma and airways, especially when combined with computer simulations, could lead to a better understanding of the structural alterations during the progression of COPD and help identify subjects at a high risk of severe COPD.