In general, charge migration can occur via pure electron electron correlation and relaxation or via coupling with nuclear motion. We must understand both aspects of charge migration through the non-hydrogen noncovalent bonds to harness full potential of the halogen-, chalcogen-, pnicogen-and tetrel-bonded photosensitive functional materials. This feature article, however, is focused on the pure relaxation- and correlation-driven charge migration, subsequent charge localization, and finally on charge-directed reactivity in the non-hydrogen noncovalent bonded clusters. Pure relaxation- and correlation-driven charge migration can occur on a several hundred attosecond (as) time scale, and this is why chemical dynamics associated with this pure electronic charge migration can be named "attochemistry". One of the efficient ways to elucidate the attochemistry is via the vertical ionization by monitoring a nonstationary electronic charge density that evolves in time while the nuclear configuration remains unchanged. So far, attochemistry of several halogen-, chalcogen-, pnicogen-, and tetrel-bonded clusters has been studied theoretically by our group. All the interesting predictions have been summarized in this Feature Article. The time scales of relaxation- and correlation-driven charge migration through the halogen, chalcogen, pnicogen, and tetrel noncovalent bonds are found to be quite similar (approximately in the range of 300-600 as) in different (1:1) AX:NH3 and AX:OH2 complexes (where A represents different substituents, such as NH2, CN, etc.). Basis sets do not exhibit any effect on the predicted charge migration time scale. A very long intermolecular distance (approximately more than 10 A), for which (physically) no noncovalent bonding interaction can be present, ceases the intermolecular charge migration. The strength of the electron electron correlation interaction influences the charge migration through these noncovalent bonds, making charge migration faster with a higher correlation interaction. The initial nuclear configuration affects the charge migration through the non-hydrogen noncovalent bonds. For large clusters, in which both hydrogen and non-hydrogen noncovalent bonds are formed, non-hydrogen noncovalent bonds are found to facilitate the charge migration preferentially over the hydrogen bonds. As a result of nuclear wavepacket delocalization, the attosecond charge oscillation in noncovalent bonded clusters decoheres. This renders charge localization. Subsequent charge-directed reactivity is discussed. This article is the first review on the attochemistry of non-hydrogen noncovalent bonded clusters.