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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

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The characterization of the physical and chemical properties of transition metals and their compounds under extreme conditions of pressure and temperature has always attracted the interest of a wide scientific community. Their properties have numerous implications in fields ranging from solid-state physics, chemistry, and materials science to Earth and planetary science. The present Special Issue represents a good example of such a broad interest and shows some of the latest advancements in the investigation of transition metals under extreme conditions of pressure and temperature.

vanadate --- kagome compound --- high pressure --- X-ray diffraction --- equation of state --- iodate --- infrared spectroscopy --- phase transitions --- grain refinement --- mechanical properties --- commercial purity aluminum --- zirconium --- Nb3Sn --- local atomic structure --- XAFS --- melting curves --- laser-heated diamond anvil cell --- extreme conditions --- synchrotron radiation --- transition metals --- iridium --- laser heating --- density-functional theory --- melting --- radial-distribution function --- quantum molecular dynamics --- melting curve --- solid–solid phase transition boundary --- multi-phase materials --- phase relation --- Earth’s core --- iron alloys --- high-pressure --- high-temperature --- thermodynamics --- eutectic spacing --- Al-Si alloy --- superheat --- electrical resistivity --- iron sulfides --- high temperature --- Ganymede --- thermal convection --- creep testing --- ME21 --- magnesium alloy --- size effects --- miniature specimen --- PbTe --- substitutional disorder --- thermal expansion --- bulk modulus --- atomic displacement --- low temperature --- compression --- Debye temperature --- n/a --- solid-solid phase transition boundary --- Earth's core