Morphometrics has been pursued by graphical and computational means since the European Renaissance, drawing on core geometric principles first discovered in China and Classical Greece. Through the late 1800s, two distinct approaches to such analyses were pursued: a deformationist approach, epitomized by D’Arcy Thompson’s graphical trans-formation grids and the statistical approach popularized by Francis Galton, Karl Pearson, and Julian Huxley in which Cartesian spaces were employed to summarize patterns of variation in size and/or shape variables. Unification of these approaches was an oft-stated goal throughout the 20th century, but proved elusive until the mid-1980s when David Kendall, Fred Bookstein, and Colin Goodall proposed a radically new way of understanding form — as the locations of configurations of landmarks on the surfaces of a nested series of hyperdimensional manifolds. Once this new mathematics of form was understood development of basic concepts, procedures, graphical tools, and statistical tests followed quickly such that the core of the long-hoped for synthesis took less than a decade to achieve. The result — geometric morphometrics — continues to develop into an ever-more extensive toolkit that can be used by researchers to describe and understand a wide range of problems involving the characterization of morphological similarities and differences in all of their many and varied contexts. In particular, the new approaches involving the direct analysis of image pixels and new tools such as machine learning and artificial intelligence are set to reinvigorate (and possibly to revolutionize) the field once again.