An overview of the recent bond-order and entropy/information measures of the chemical bond mul- tiplicity and of its covalent/ionic composition is given. The former include the Wiberg index of the molecular orbital (MO) theory and its atomic/diatomic components, while the latter explore the communication-noise (covalency) and information-flow (ionic) descriptors of molecular infor- mation channels in the atomic-orbital (AO) resolution. The illustrative application to the two -orbital model is presented and the atomic resolution of bond contributions is pre- sented. Alternative information distributions, including densities of the displacement in the system Shannon entropy and its entropy deficiency relative to the ‘‘pro- molecule,’’ are advocated as effective probes of chemical bonds. They complement the familiar density difference diagrams of electron redistributions accompanying the bond formation process. These quantities are applied to investigate the central bond in small propellanes and the contragradience criterion, based upon the non -additive Fisher information in electron distribution, is shown to efficiently locate the bonding regions in butadiene and benzene. The novel, indirect bonding mechanism through the orbital intermediaries, inferred from the orbital com- munication theory in the AO resolution, is probed in these two illustrative p -electron systems using the generalized Wiberg bond-orders. It is shown to give rise to a more realistic representation of the second -neighbor interactions, which have previously been diagnosed as the direct (through- space ) non -bonding. In MO theory, these through- bridge bond components are due to the implicit dependencies between the ( non -orthogonal) AO projec- tions onto the molecular bonding subspace of the occupied MO. They do not require the bond-charge accumulation between the nuclei of bonded atoms and can be realized at longer distances. The effective range of such indirect interactions is probed in representative polymers. Finally, the entropy/information concepts for three dependent probability distributions are used to qualitatively examine the promotion of reactants in catalysis. The chemisorbed species are predicted to undergo an ionic promotion, compared to the gas-phase reference, thus exhibiting more deterministic communications on the catalytic surface