The crystal structures of inorganic hydroborates (salts and coordination compounds with anions containing hydrogen bonded to boron) except for the simplest anion, borohydride BH4−, are analyzed regarding their structural prototypes found in the inorganic databases such as Pearson's Crystal Data [Villars and Cenzual (2015), Pearson's Crystal Data. Crystal Structure Database for Inorganic Compounds, Release 2019/2020, ASM International, Materials Park, Ohio, USA]. Only the compounds with hydroborate as the only type of anion are reviewed, although including compounds gathering more than one different hydroborate (mixed anion). Carbaborane anions and partly halogenated hydroborates are included. Hydroborates containing anions other than hydroborate or neutral molecules such as NH3 are not discussed. The coordination polyhedra around the cations, including complex cations, and the hydroborate anions are determined and constitute the basis of the structural systematics underlying hydroborates chemistry in various variants of anionic packing. The latter is determined from anion–anion coordination with the help of topology analysis using the program TOPOS [Blatov (2006), IUCr CompComm. Newsl. 7, 4–38]. The Pauling rules for ionic crystals apply only to smaller cations with the observed coordination number within 2–4. For bigger cations, the predictive power of the first Pauling rule is very poor. All non-molecular hydroborate crystal structures can be derived by simple deformation of the close-packed anionic lattices, i.e., cubic close packing (ccp) and hexagonal close packing (hcp), or body-centered cubic (bcc), by filling tetrahedral or octahedral sites. This review on the crystal chemistry of hydroborates is a contribution that should serve as a roadmap for materials engineers to design new materials, synthetic chemists in their search for promising compounds to be prepared, and materials scientists in understanding the properties of novel materials.