The complexities of chemical composition and crystal structure are fundamental characteristics of minerals that have high relevance to the understanding of their stability, occurrence and evolution. This review summarises recent developments in the field of mineral complexity and outlines possible directions for its future elaboration. The database of structural and chemical complexity parameters of minerals is updated by H-correction of structures with unknown H positions and the inclusion of new data. The revised average complexity values (arithmetic means) for all minerals are 3.54(2) bits/atom and 345(10) bits/cell (based upon 4443 structure reports). The distributions of atomic information amounts,^chemI_Gand^strI_G, versus the number of mineral species fit the normal modes, whereas the distributions of total complexities,^chemI_G,totaland^strI_G,total, along with numbers of atoms per formula and per unit cell are log normal. The three most complex mineral species known today are ewingite, morrisonite and ilmajokite, all either discovered or structurally characterised within the last five years. The most important complexity-generating mechanisms in minerals are: (1) the presence of isolated large clusters; (2) the presence of large clusters linked together to form three-dimensional frameworks; (3) formation of complex three-dimensional modular frameworks; (4) formation of complex modular layers; (5) high hydration state in salts with complex heteropolyhedral units; and (6) formation of ordered superstructures of relatively simple structure types. The relations between symmetry and complexity are considered. The analysis of temporal dynamics of mineralogical discoveries since 1875 with the step of 25 years show the increasing chemical and structural complexities of human knowledge of the mineral kingdom in the history of mineralogy. In the Earth's history, both diversity and complexity of minerals experience dramatic increases associated with the formation of Earth's continental crust, initiation of plate tectonics and the Great Oxidation event.

The modular approach is a powerful tool in current inorganic crystal chemistry. It enables not only a more detailed analysis of the known structures and the determination of structural relationships between them, but also the prediction of potentially novel structures that can be applied in modern materials science. A large number of examples of compounds with modular structures allows us to state that structural modularity is a widely spread phenomenon among natural and synthetic compounds. The use of the formalism of OD theory makes it possible to analyze the symmetry of polytypes with different crystal structures. In this review, we collected new data published in the last 15 years about OD structures and phenomena of polytypism and modularity in inorganic compounds, as well as the topological approach to the analysis of crystal structures.