The boron hydrides, including the polyhedral boranes, heteroboranes, and their metalla derivatives, encompass an amazingly diverse area of chemistry. This class contains the most extensive array of structurally characterized cluster compounds known. Included here are many novel clusters possessing idealized molecular geometries ranging over every point group symmetry from identity (
C
1
) to icosahedral (
I
h
). Because boron hydride clusters may be considered in some respects to be progenitorial models of metal clusters, their development has provided a framework for the development of cluster chemistry in general as well as for chemical bonding theory. Because the polyhedral boron hydrides are cage molecules, which usually possess triangular faces, their idealized geometries can be described accurately as deltahedra or deltahedral fragments. These idealized structures are convex deltahedra except for an octahedron, which is not a regular polyhedron. One class represents deltahedral
closo
molecules from which the other idealized structures (deltahedral fragments) can be generated systematically. Any
nido
or
arachno
cluster can be generated from the appropriate deltahedron by ascending a diagonal from left to right. This progression generates the
nido
structure by removing the most highly connected vertex of the deltahedron, and the
arachno
structure by removal of the most highly connected atom of the open (nontriangular) face of the
nido
cluster. The terms
closo, nido, arachno
, and
hypho
are derived from Greek and Latin and imply closed, nestlike, weblike, and netlike structures, respectively. These classifications apply equally well to boranes, heteroboranes, and their metalla analogues, and are intimately connected to a quantity known as the framework, or skeletal, electron count. The partitioning of electrons into framework and exopolyhedral classes allows for predictions of structures in most cases. Many of the deltahedra and deltahedral fragments have two or more nonequivalent vertices. Nonequivalent vertices are recognized as having a different order; ie, a different number of nearest neighbor vertices within the framework. Heteroatoms generally exhibit a positional preference based on the order of the polyhedral vertex and the electron richness of the heteroatom relative to boron. The placement of extra hydrogens plays a crucial role in determining the structures adopted by boranes and carboranes. The placement of bridge hydrogens may be the most important variable in the determination of relative isomer stabilities, outranking placement of heteroatoms. Numerous metallaboranes and metallaheteroboranes are known to contain hydrogens bridging between a metal atom and a skeletal boron atom, but complexes containing covalently bound tetrahydroborate(
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),
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, constitute the prototypical class. When strong electron‐donating or withdrawing groups are present there is the possibility of structural anomalies. Some metallacarboranes also present anomalies to the electron‐counting formalisms. Because boron hydrides have more valence orbitals than valence electrons, they have often been called electron‐deficient molecules. This electron deficiency is partly responsible for the great interest surrounding borane chemistry and molecular structure. The elucidation of the structure of diborane(6) led to the description of a new bond type, the three‐center bond, in which one electron pair is shared by three atomic centers. The delocalization of a bonding pair over a three‐center bond allows for the utilization of all the available orbitals in an electron‐deficient system. Nido and arachno boranes are generally more reactive and less stable thermally than the corresponding
closo
boranes. The
nido
and
arachno
boranes smaller than B
10
H
14
are quite reactive toward oxygen and water. In addition to the localized bond descriptions, molecular orbital (MO) descriptions of bonding in boranes and carboranes have been developed. Molecular orbital descriptions are particularly useful for
closo
molecules where localized bond descriptions become cumbersome because of the large number of resonance structures that do not accurately reflect molecular symmetry. Certain base adducts of borane, BH
3
, such as triethylamine borane,
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, dimethylsulfide borane,
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, and tetrahydrofuran borane,
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, are more easily and safely handled than B
2
H
6
and are commercially available. These compounds find wide use as reducing agents and in hydroboration reactions. A variety of boranes, heteroboranes, and metallaboranes undergo electrophilic substitution. Just as the previously known boron hydrides might be considered as analogues of aliphatic hydrocarbons, the
closo
borane anions are analogues of aromatic hydrocarbons. The best known members of this series,
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and
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, have been the subject of detailed studies. The tetrahydroboranes constitute the most commercially important group of boron hydride compounds. Tetrahydroborates of most of the metals have been characterized and their preparations have been reviewed. The important commercial tetrahydroborates are those of the alkali metals. The use of tetrahydroborates, as well as the boranes and organoboranes, for organic transformations has proven to be significant because these reduction reactions are highly selective and nearly quantitative. Borohydrides are often the reagents of choice for the reduction of aldehydes and ketones to the corresponding alcohols. Many other functional groups, such as acid chlorides, imines, and peroxides, can also be reduced using borohydrides. Heteroboranes contain heteroelements classified as nonmetals. The heteroatoms known to form part of a borane polyhedron include C, N, Si, P, As, S, Se, Sb, and Te either alone or in combination. Extensive chemistry has emerged only for the thiaboranes and azaboranes, which have the greatest availability and demonstrated scope of chemistry. The term carborane is widely used in the American literature as a contraction of the IUPAC‐approved nomenclature carbaborane. The discovery of the icosahedral
closo
‐1,2‐dicarbadodecaborane(12), 1,2,‐C
2
B
10
H
12
, led to a rapid development of carborane chemistry. The discovery of the base‐promoted degradation of the isomeric
closo
‐C
2
B
10
H
12
cages provided one of the most important carborane anion systems, the isomeric
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anions. Commonly referred to as dicarbollide ions, derived from the Spanish olla, meaning a bowl, the dicarbollide anions, aside from their extensive use in metallacarborane chemistry, are important intermediates in the synthesis of other carborane compounds. Cage rearrangements in polyhedral carboranes have been studied. Many of the carborane isomers obtained by conventional synthetic routes are kinetic products and not the thermodynamically most stable isomers. A diversity of polyhedral carborane cage‐containing polymers has been prepared. The best known of these are elastomeric polycarboranylsiloxanes. Some of these materials have excellent thermal stabilities, chemical resistance, and high temperature elastomeric properties. Polymers of this type, known under the trade name Dexsil, are commercial materials, useful as stationary phases in gas chromatography. Other well‐documented families of heteroboranes include the azaboranes, phosphaboranes, arsenaboranes, stibaboranes, selenaboranes, and telluraboranes. By 1990 a great many
nido
metallaborane clusters has been characterized covering a wide range of sizes and polyhedral fragment geometries. The first
closo
metallaborane complexes prepared were the nickelaboranes
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and
closo
‐1,2‐(η
5
‐C
5
H
5
)
2
‐1,2‐Ni
2
B
10
H
10
. These metallaboranes display remarkable hydrolytic, oxidative, and thermal stability. A number of novel products have been isolated from the reaction of
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and CoCl
2
and
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in THF. Also obtained are isomeric clusters containing up to four cobalt atoms, eg, (η
5
‐C
5
H
5
Co)
4
B
4
H
8
, indicating an unusual 2
n
framework electron count having geometries reminiscent of strictly metallic clusters. A variety of metallaborane clusters, which incorporate main group metals in vertex positions of polyhedral metallaborane clusters, have been reported. The isomeric
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ions, which are commonly known as dicarbollide ions, and many other carborane anions, form stable complexes with most of the metallic elements. Indeed, nearly all metals can be combined with polyborane hydride clusters to produce an apparently limitless variety of cluster compounds. Many metallacarboranes are known that exhibit exopolyhedral bonding to metals. Perhaps the most intensely studied of all metallacarborane complexes is the exopolyhedral metallacarborane
closo
‐3,3‐[P(C
6
H
5
)
3
]
2
‐3‐H‐3,1,2‐RhC
2
B
9
H
11
. The three available isomers of
closo
‐[P(C
6
H
5
)
3
]
2
(H)Rh‐C
2
B
9
H
11
are synthesized in high yield by the oxidative addition of [P(C
6
H
5
)
3
]
2
RhCl with the appropriate
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ion. The resulting hydridorhodacarboranes are quite robust and catalyze a number of reactions, including the isomerization and hydrogenation of olefins, the deuteration of B–H groups, and the hydrosilanolysis of alkenyl acetates. These species function as homogeneous catalyst precursors for the isomerization and hydrogenation of olefins as well as other reactions. Main group element carborane derivatives have been reviewed, as have
f
‐block element metallacarborane derivatives. One of the most promising applications of polyboron hydride chemistry is boron neutron capture therapy (BNCT) for the treatment of cancers. The challenge of BNCT lies in the development of practical means for the selective delivery of approximately 10
9
10
B atoms to each tumor cell. Derivatives of
10
B‐enriched
closo
‐borane anions and carboranes appear to be especially suitable. New generations of tumor‐localizing boronated compounds are being developed. A related potential medical application of metallacarboranes is based on their highly favorable kinetic stability under physiological conditions, making certain functionalized metallacarboranes containing radiometals ideal choices for use as medical imaging reagents. Only the simplest of boron hydride compounds, most notably sodium tetrahydroborate, Na[BH
4
], diborane, B
2
H
6
, and some of the borane adducts, eg, amine boranes, are now produced in significant commercial quantities. Sodium tetrahydroborate, Na[BH
4
], an air‐stable white powder commonly referred to as sodium borohydride, is the most widely commercialized boron hydride material. It is used in a variety of industrial processes, including bleaching of paper pulp and clays, preparation and purification of organic chemicals and pharmaceuticals, textile dye reduction, recovery of valuable metals, wastewater treatment, and production of dithionite compounds. Diborane(6), B
2
H
6
, a spontaneously flammable gas, is consumed primarily by the electronics industry as a dopant in the production of silicon wafers for use in semiconductors. Trialkylamine and dialkylamine boranes, such as tri‐
t
‐butylamine borane and dimethylamine borane, are mainly used in electroless plating processes. Polyhedral boron hydrides and carboranes are used in neutron capture therapy of cancers, and as burn rate modifiers (accelerants) in gun and rocket propellant compositions. Metallacarboranes are used in homogeneous catalysis, including hydrogenation, hydrosilylation, isomerization, hydrosilanolysis, phase transfer, burn rate modifiers in gun and rocket propellants, neutron capture therapy, medical imaging, processing of radioactive waste, analytical reagents, and as ceramic precursors.