Polyiodides have long 1,2 been a classic among scientifically challenging systems for chemists and physicists alike. Structural chemistry and geometrical possibilities displayed by polyiodides are particularly rich. To such a richness subtends complexity: even the simplest of polyiodides, I3 -, was immediately recognized as an anion defying the octet rule. The apparent violation of octet rule has led to a mainstream explanation of polyiodides as hypervalent species and has played a pivotal role in the understanding of, and/or constitutes a prime example of, three-center-four-electron (3c-4e) bonds. On the other hand, polyiodides with a larger number of atoms in the chain than I3 -also possess interesting alternation in terms of bond lengths, with many I … I bonds(?)/ contacts(?)/ interactions(?) that fall in an intermediate region between single covalent (2c-2e bonds, like in I2) bonds and supramolecular interactions, which are, nevertheless, strongly directional. For this very reason, polyiodides have been a prime crucible for the elaboration of novel concepts, in general, in inorganic, physical, and also supramolecular chemistry. In the latter realm, namely, secondary bonds and halogen bonds (and actually further models in between) are here of special relevance. To that end, polyiodides have been generally approached with a reductionist approach, dismantling superior species in terms of complexes of the I2, I -, and I3 - reassuring basic building blocks, often via an I … I experimental distance-based approach to differentiate them in covalently-, secondary-/halogen-, and non-bonded fragments. Such is, in a nutshell, the summary of the first two centuries of polyiodide history. What can we possibly add to this? What can have changed recently to prompt us to rethink it all? Three facts: i) supramolecular interaction models, old (secondary bond) and new (halogen bonds), started being criticized both on experimental and theoretical grounds (see discussion herein and in refs. 8,18 for an overview); ii) the need and possibility of coherently rebuilding a view of related supramolecular interactions were advanced and contact points highlighted; and iii) an apparently innocent-yet-revolutionary statement recently made: linear multicenter bonds on more than 3 atoms must be of the electron-deficient type (i.e. 2c-1e electron-deficient multicenter bonds, or EDMB), even for electron-rich elements, such as I, with plenty (7) of valence electrons. Herein we start from the contributions of Manjón and coworkers about the nature of bonding in chain-type systems, present in pnictogens and chalcogens, as well as in halides, and work our way to re-understand polyiodides bonding and geometries. These same observations -to different extents, stemming from different backgrounds, and reaching a variety of conclusionsare simultaneously emerging in very recent work of several research groups around the world, especially for halogen-related systems. We will briefly attempt to re-explain polyiodides below using a revisited version of Lewis dot formulas. On these grounds, we will then re-discuss and re-think current models for polyiodides and iodine-iodine bonds and interactions.