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Today all structural information of the lung can be quantified and interpreted in the three-dimensional space of real-world biology. Remarkable achievements in the theory and practice of biological stereology are creating a new generation of data suitable for constructing structural hierarchies. Such hierarchies serve to organize and link biological data, thereby providing a framework on which to build new information systems. In this review, we describe the new tools of quantitative morphology and show how they can be used to design new experiments for lung research.