What is the genetic basis of phenotypic variants? What is the anatomical substrate of cognitive loss? How does pathology affect brain development and to which extend do treatments modify disease onset? What distinguishes normal aging from pathological brain atrophy? Such key questions raise the need for efficient methods to automatically analyze phenotypic variants in series of 3D anatomical data. Methods based on images often lack statistical power and their results are difficult to interpret, whereas methods based on anatomical shapes extracted from images are based on point correspondence, which requires intensive pre-processing and limits its use in large cohort studies. In this talk, we will present a unified approach to morphometry, which deals with data complexes made of images, points sets, curves, surfaces or any combination of them. Variations of such complexes are integrated into a unique space deformation of the underlying anatomy. Therefore, our method considers only anatomically realistic variations that preserve the local organization of the tissues, thus introducing constraints in measures of correlations between components in the complex. Shape invariants that are found consistently across the samples are integrated into a template complex, which has the same form as the samples. Typical phenotypic variations of the template complex are quantified by the deformation parameters. Finite-dimensional parameterization of deformations is proposed, which automatically adjusts to focus on the most variable parts of the anatomy. We will show that statistics derived from these parameters could separate populations with very high sensitivity and specificity. Besides quantitative results, the use of deformations enables also to display the most discriminative variants in an interpretable way. The estimation of the deformations uses the metric on currents or varifolds which make possible the comparison of meshes with different sampling, topological imperfections and numerical noise, thus minimizing the need of user intervention. The method could be used in various contexts on a routine basis, for instance, to find early anatomical biomarker of disease onset, to study pathophysiology or for taxonomic purposes.