Ab initio computations are performed to investigate properties of bulk material and epitaxial films made of EuTiO3 (ETO). A whole family of nanoscale twinned phases, that present complex oxygen octahedra tilting (OOT) and unusual antiferroelectricity, is found to be degenerate in energy with simpler phases (all possessing typical OOT) in bulk ETO. Such degeneracy provides a successful explanation of recently observed anomalous phenomena. The calculations also lead to revisiting the (rich) phase diagram of ETO films.