The concept of aromaticity has dramatically evolved and expanded to where it is no longer reserved for use in organic chemistry but is also useful in describing the bonding in many inorganic compounds. The aromaticity of inorganic rings arises from participation of s, p, d and f atomic orbitals to form delocalized σ, π, δ and φ molecular orbitals. This report describes the stability, structures and bonding of mainly covalent inorganic “sandwich” compounds or metallocenes in which aromatic, antiaromatic and nonaromatic inorganic rings, as well as those with multiple or conflicting aromaticity, are bonded primarily to the transition elements. Also included are some examples of ionic salt and covalent metallocenes of the main group and f-block elements with rings that exhibit other than only p orbital aromaticity. While many of the referenced compounds have been experimentally generated, computational methods play an important role in predicting the stability and ground state structures of several other hypothetical inorganic rings and the metallocenes produced from them. The theoretical studies also aid in defining the criteria that are used in determining the nature of compound aromaticity.