Deformations of cell sheets are ubiquitous in early animal development, yet they arise from an intricate interplay of cell shape changes, cell migration, cell intercalation, and cell division. We combine theory and experiment to explore what is perhaps the simplest instance of cell sheet folding, the "inversion" process in the green alga Volvox: at the end of cell division, a Volvox embryo consists of several thousand cells arrayed to form a thin spherical sheet, but those cell poles whence will emanate the flagella point into the sphere. In a process hypothesised to arise from cell shape changes alone, the embryos therefore turn themselves inside out to acquire the ability to swim. We have recently acquired the first three-dimensional time-lapse visualisations of this inversion, using light sheet microscopy to reveal the intriguing dynamics of the process. A theoretical model, in which cell shape changes correspond to local variations of intrinsic curvature and stretches of an elastic shell, sheds light on the underlying mechanics of inversion and reproduces the shapes and dynamics of inversion qualitatively. This is joint work with Stephanie Höhn, Aurelia Honerkamp-Smith, Philipp Khuc Trong and Ray Goldstein.