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 summarizes 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) bit/atom and 345(10) bit/cell (based upon 4443 structure reports). The distributions of atomic information amounts, chemIG and strIG, versus the number of mineral species fit the normal modes, whereas the distributions of total complexities, chemIG,total and strIG,total, as well as numbers of atoms per formula and per unit cell are lognormal. The three most complex mineral species known today are ewingite, morrisonite and ilmajokite, all either discovered or structurally characterized within the last five years. The most important complexity-generating mechanisms in minerals: (i) the presence of isolated large clusters; (ii) the presence of large clusters linked together to form three-dimensional frameworks; (iii) formation of complex three-dimensional modular frameworks; (iv) formation of complex modular layers; (v) high hydration state in salts with complex heteropolyhedral units; (vi) 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.