The concept of a chemical bond has long been intensely debated. On the one hand, it encapsulates our understanding of matter's existence and stability. On the other hand, it lacks a quantitative measure to establish whether two atoms are chemically bonded, making it a non-physical observable. This dichotomy has led to various methodologies to decipher this elusive construct. In 1916 proposed that a chemical bond could be interpreted as an electron pair shared by two atoms, an idea that has since profoundly ingrained itself in the minds of chemists. Fifteen years later, Pauling translated Lewis sharing idea into the emerging quantum mechanics language, building on Heitler and London's work. Bader and Henneker 11 used the electric field to explore a completely different interaction -the ionic bond. Gadre and co-workers combined this field with topological concepts to describe various bonding situations in neutral and electrically charged molecular systems. Researchers have sought conclusive evidence for decades to resolve the dichotomy between the relevance of kinetic and potential energies in chemical bonding. Bader's seminal work on the topological analysis of the electron density introduced a new way to gain insights into the characterization of the chemical structure and bonding concepts. This method has also been applied to other local functions, including the electron localization function (ELF), the nuclear potential, the virial field, the magnetically induced molecular current distribution, and the spin density. Such type of analysis has been proposed to be classified as quantum chemical topology (QCT). QCT leverages the topographical analysis of the gradient vector field generated by scalar functions to extract valuable chemical information without explicitly mentioning the reference state. These approaches enable a definition of topological domains using partitioning schemes, which are parameter-free. Krokidis, Noury, and Silvi explored for the first time the application of Thom's catastrophe theory (CT) to the analysis of topographical changes of ELF along a given coordinate, i.e., defining the so-called bonding evolution theory (BET) methodology. BET has been applied in an ever-increasing fashion over the last three decades to gain a deeper understanding of different covalent bonding situations, C-H bonds activation, proton transfer reactions, cycloadditions, phase transition of the 14 group elements, hemiaminals formation, computing local and global properties of solids, and deducing linear models for predicting activation enthalpies of organic and organometallic systems.