Since 2010, theoretical studies using first-principles calculations based on density functional theory (DFT) and advanced imaging techniques, such as high-resolution transmission electron microscopy (HR-TEM), have significantly advanced understanding of vaterite crystal structures. Light atoms such as carbon and oxygen in CO 3 2can be detected using annular bright-field and atomic-resolution high-angle annular dark field (ADF) microscopy, producing clear diffraction images of microscopic regions. Spectroscopic techniques, including Raman and Ca solid-state nuclear magnetic resonance (NMR), have further refined the understanding of vaterite structures. An excellent review summarized these find-ings and proposed six plausible vaterite polytypes. These crystal systems include trigonal and monoclinic structures with varying stacking sequences of CO 3 2in the interlayer space of Ca 2+ sheets. Recent ADF and machine-learning-aided molecular dynamics (MD) simulations have suggested plausible structures with C2/c and C2 SGs, depending on temperature. Studies in the 2010s significantly accelerated the general understanding of vaterite structures in biologically derived or highly crystalline synthesized vaterites. However, vaterite found in cementitious materials and biological substances 4,15-17 often exhibits low crystallinity, suggesting numerous structural possibilities, including amorphous CaCO 3 phases. Minerals classified as vaterite in cementitious materials likely exhibit diverse structures, including lattice distortions, dislocations, and defects. Thermodynamically unstable vaterite is highly susceptible to environmental factors, resulting in polytypic variations during crystal growth and surface interactions in nanoscale particles.