**1. Introduction**

In recent years, wonderful molecular features have emerged through the study of pure and atom-doped boron clusters. Boron is a *p*-element that has three valence electrons and one of them in the *p*-orbital. Also, this element is located between the metallic and nonmetallic elements of the periodic table and, like carbon, is an exceptional element with a self-catenation character. Boron can form bonds between the same elements leading to the synthesis of the pure hydride of boron compounds. Also, it scarcely obeys the octet rule, and its valence shell typically contains only six electrons.

The main family of boron compounds is classified into two different branches: (i) the boron clusters that can form carboranes, borohydrides, metallacarboranes, and (ii) the organic compounds, in which they structures are different and their characteristics depend on the size. Although the organic compounds contain chains and rings, the boron clusters have a planar or cage-like structures. Also, the boron clusters have various shapes and symmetries that are the result of occupying vertices through different numbers of boron atoms or heteroatoms. The shape of these clusters is widespread, from unstable tetrahedral to more stable icosahedral [1, 2].

According to these intrinsic features, the chemical properties of boron clusters have gained great attention from researchers. To date, 16 polymorphs have been detected for bulk boron. Among them, the B12 icosahedron is a predominant motif [3]. However, it is shown that B12 cluster in isolated form is not stable and tends to form planar or quasiplanar structures. The anionic and cationic forms of the small boron clusters (B*n*; *n*≤ 36) usually prefer to have planar and two-dimensional structures, respectively.

The planar structures in the edge consist of two-center two-electron (2c-2e) sigma bonds and between the inner atoms have multicenter two-electron (nc-2e) bonds. Multidimensional aromaticity as a result of delocalized *σ* and *π* bonds is responsible for the stability, planarity, and bioavailability of planar boron-based clusters. Furthermore, energetically favorable 1D boron nanotubes [4] and 2D boron sheets [5–7] have been produced, and their structure contains planar triangular lattices with hexagonal holes.

By discovering the cage-like structure of B40/B� 40, a new family is introduced to the boron cluster which is called borospherene. These hollow structures are generally interlocking boron chains formed from trigonal fragments and containing holes with hexa, hepta, and other sizes. Also, planar B36 is a pioneer in the borophene concept having a monolayer structure with hexagonal vacancies. The smallest borospherene that has been discovered is B� <sup>28</sup> and other motifs for borophene are B� 26, B� 35, B� 37, and B� 38.

Experimental and theoretical studies revealed that 0D boron clusters with B� *<sup>n</sup>* (*n*< 38) structure are planar and quasi-planar, and their stability is the result of delocalized multicentric bonding [8–11]. They also demonstrated that the B*<sup>n</sup>* (31≤ *n* ≤50) clusters can have a tubular structure [10]. Series of axially chiral borospherenes structures for B<sup>þ</sup> 38, B<sup>2</sup><sup>þ</sup> <sup>38</sup> , B<sup>þ</sup> 31, and B32 clusters are also investigated [12, 13]. In a boron cluster of a certain size with a large number of boron atoms, the structures proposed for its ground state are cage-like [14], quasi-planar, and bilayer (i.e. B� 48) [15–17]. Moreover, for B*<sup>n</sup>* clusters with *n*> 68, the most energetically stable structure is found to be core-shell [18].

Replacing a boron atom with a specific dopant leads to the production of a new subclass that is of particular interest and diverse in structure. For example, transition metal doping of B*<sup>n</sup>* (12≤ *n* ≤ 22) clusters forms metal-centered monocyclic boron rings [19–22], half-sandwich structures in metal-doped B*<sup>n</sup>* clusters [23, 24], inversesandwich structure in La-doped B� *<sup>n</sup>* cluster [25], and endohedral boron cage in NiB80 cluster [26]. However, a new way to achieve intriguing features in boron clusters can be constructed by a specific combination of the number of doped atoms and boron atoms in the boron clusters.

The variety in boron clusters and their atom-doped counterparts has increased the ability of these clusters to be applied in different applications. As such, in this chapter, to generate new insights into the various applications, we review some important applications of boron clusters and their atom-doped counterparts. We will briefly introduce the most relevant computational methods to simulate these clusters and then present examples of their use in different areas, ranging from drug delivery to reaction catalysis. We hope to inspire the general community and research groups to get involved in proposing new applications for boron clusters.
