Boron minerals are among the most structurally and chemically complex naturally occurring inorganic compounds. Of the 291 B minerals recognized as valid or potentially valid, structures are known for 256 species (plus three polytypes); for 245 of these the age of the earliest reported occurrence in the geologic record has also been reported. The earliest B minerals are four tourmaline species formed during metamorphism at 3550 Ma in the Isua supracrustal belt (Greenland), but many ephemeral B minerals are restricted to Late Cenozoic and Holocene deposits. We analyzed structural complexity with the program package TOPOS, using complexity parameters that provide Shannon information content per atom and per unit cell (Krivovichev 2013). The average content per unit cell, 343 bits/unit cell (hereafter noted simply as “bits”), is significantly greater than the mode complexity (ca. 175 bits) because distribution of complexity is strongly right-skewed. Qingsongite, cubic BN (2 bits), is the simplest boron mineral. Seventeen B minerals possess information content per unit cell > 1000 bits. Rogermitchellite, Na6(Sr,Na)12Ba2Zr13Si39(B,Si)6O123(OH)12·9H2O, which is the most complex (2321 bits), owes its structural complexity in part to the incorporation of eight essential chemical elements. However, chemically simpler hydrated Ca borates (with four or five essential elements), e.g., ginorite, Ca2B14O20(OH)6·5H2O (1506 bits); ruitenbergite, Ca9B26O34(OH)24Cl4·13H2O (1492 bits); and alfredstelznerite, Ca4B16O16(OH)24·19H2O (1359 bits), are also structurally complex, which we attribute to the interplay of borate polyanions and hydrogen bonding networks. The earliest complex borates are takéuchiite (1179 bits), blatterite (1656 bits), and the Mg analogue of blatterite (1612 bits), which are reported uniquely from 1825 Ma deposits at Långban and Nordmark (Sweden). There is little evidence for a significant increase in maximum structural complexity since 1825 Ma. Localities with high boron mineral diversity (nine to 25 species) are more likely to contain minerals with complex structures, which could be simply a matter of there being more minerals present, which increases the chance that one of these minerals would be structurally complex. The variation of structural complexity with time shows features of a “passive” trend in mineral evolution – more minerals with complex structures arise with the passage of geologic time, yet the simpler structures are not supplanted; instead, new simpler structures also appear, e.g., tourmaline-supergroup minerals (176 to 207 bits).