This work presents chemical applications of topological methods in various sectors, from small
molecule to biological systems, in studying for example enzyme-catalyzed reaction, protein folding kinetics,
DNA sequence characterization. Topological descriptors participate to QSAR/QSPR models and, furthermore,
are able to individuate the regions which are stabilized (or, vice versa, made reactive) by certain topological interactions.
The Wiener indexes, and other distance-based invariants, constrained by the minimum-principle,
oppose any unfavorable topological variation in the molecular structure (e.g. chemical transformations). Topological
models characterize therefore chemical structures with astonishing details with computational simplicity predicting novel chemical
mechanisms to be confirmed by subsequent ab-initio studies. Reported topological methods for simulating complex chemical mechanism
and interesting chemical structures preserve the “usual” computational simplicity and still carry a large amount of chemical information
stored in topology, an evident alliance between chemistry and mathematics in explaining how the nano-world works.