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The articles published in this Special Issue reprint offer a sound update of research fields where the concepts of modular crystallography are important and provide unique keys to understand and to solve problems of structural crystallography. Polytypism, polysomatism, and twinning are fertile fields of research, and their basic principles—often coupled with the OD (order-disorder) theory—are powerful tools to solve and classify related crystal structures. Research on twinning and its consequences on structure and properties of crystalline materials is cutting-edge, e.g., dealing with relations between twin walls and piezoelectricity.

tetrahedrite --- tennantite --- twinning --- order–disorder approach --- tetrahedral framework --- modular structures --- polysomes (series) --- synthetic analogues of minerals --- transition metal phosphates --- X-ray diffraction --- antiferromagnets --- frustrated magnets --- kagomé lattice --- chemical ordering --- superstructure --- spryite --- argyrodite-type compounds --- ultra-low temperature --- RE-silicate-germanate --- hydrothermal synthesis --- layered silicates --- modular approach --- wollastonite chain --- topology-symmetry analysis --- OD theory --- structure prediction --- luminescence properties --- twin wall --- twin boundary --- minerals --- emerging properties --- piezoelectricity in minerals --- surface relaxations --- anorthite --- Pamierite --- perovskite --- OD structures --- polytypism --- polymorphism --- heteropolyhedral framework --- modularity --- topology --- borophosphates --- aluminophosphates --- DFT --- electron diffraction --- c-type reflections --- ordering --- calcite --- glendonite --- TEM --- n/a --- order-disorder approach --- kagomé lattice