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This minisymposium will focus on the fundamental and applied aspects of shape analysis. Shape analysis remains one of the key problems to many recent applications ranging from automatic object recognition in computer vision to the field of biomedical imaging in which datasets typically involve multiple geometric structures with important morphological variability. Modern methods are at the intersection of several fields in mathematics that span finite and inifinite dimensional geometry, optimal control, optimal transport and statistical data analysis. The objective of the mininisymposium is to bring together researchers covering those multiple aspects to present most recent ideas in the field, discuss new directions of interest for the community and foster future collaborations across different groups.