U nlike solid organs, the lung is a hollow organ that contains, under physiological conditions, an amount of air that is much larger than the total amount of its tissue. This confers to the lung a degree of heterogeneity that is much larger than in any other organ and adds difficulties to the interpretation of physiological measurements, which are in most cases related to the whole system. To overcome these difficulties and to construct suitable models for lung function, a number of studies on the relationships between structure and function have been performed over the last five decades. The major problem in relating lung function measurements to morphological data is the need to gather information on a three-dimensional (3D) structure from two-dimensional (2D) observations. Although data from simple 2D images have been widely used to describe pathological changes in lung parenchyma or airways, their relevance to physiological events occurring in 3D structures is limited.The key to obtaining valuable 3D morphometric data from 2D measurements is provided by stereology. This method had its foundations lain in 1777 by G. Buffon, who discovered the relationships between geometry and probability [1]. This opened the way for classical model-based stereology, which required an assumption of homogeneity of 3D structure. Stereology was first applied to medicine in the 1940s and to respiratory systems in 1952 by CAMPBELL and TOMKEIEFF [2], who calculated the internal surface of the lung.Major advances in lung quantitative morphometry were bestowed by WEIBEL and co-workers [3][4][5][6] between the 1960s and 70s. They provided the basic tools for modern designbased stereology. This is particularly suitable for the lung, as it can be applied to structures that are inhomogeneous or cannot be assumed to be homogeneous. Despite this and the subsequent developments made towards obtaining unbiased quantitative data of inhomogeneous structures, such as lung parenchyma and the bronchial tree, stereology has been used less in pulmonary research than in other fields.In recent years, the European Respiratory Society (ERS) has organised two courses dedicated to quantitative morphology in pulmonary research, followed by a series of articles in one issue of the European Respiratory Review which offered insight into the theoretical principles and practical applications of design-based stereology to graduate students and scientists [7][8][9][10][11][12][13].