The bonding in the highly homoatomic np(pi)-np(pi) (n >= 3)-bonded S2I42+ (three sigma + two pi bonds), the Se-I pi-bonded Se2I42+ (four sigma + one pi bonds), and their higher-energy isomers have been studied using modern DFT and ab initio calculations and theoretical analysis methods: atoms in molecules (AIM), molecular orbital (MO), natural bond orbital (NBO), and valence bond (VB) analyses, giving their relative energies, theoretical bond orders, and atomic charges. The aim of this work was to seek theory-based answers to four main questions: (1) Are the previously proposed simple pi*-pi* bonding models valid for S2I42+ and Se2I42+? (2) What accounts for the difference in the structures of S2I42+ and Se2I42+? (3) Why are the classically bonded isolobal P2I4 and As2I4 structures not adopted? (4) Is the high experimentally observed S-S bond order supported by theoretical bond orders, and how does it relate to high bond orders between other heavier main group elements? The AIM analysis confirmed the high bond orders and established that the weak bonds observed in S2I42+ and Se2I42+ are real and the bonding in these cations is covalent in nature. The full MO analysis confirmed that S2I42+ contains three sigma and two pi bonds, that the positive charge is essentially equally distributed over all atoms, that the bonding between S-2 and two I-2(+) units in S2I42+ is best described by two mutually perpendicular 4c2e pi*-pi* bonds, and that in Se2I42+, two SeI2+ moieties are joined by a 6c2e pi*-pi* bond, both in agreement with previously suggested models. The VB treatment provided a complementary approach to MO analysis and provided insight how the formation of the weak bonds affects the other bonds. The NBO analysis and the calculated AIM charges showed that the minimization of the electrostatic repulsion between EI2+ units (E = S, Se) and the delocalization of the positive charge are the main factors that explain why the nonclassical structures are favored for S2I42+ and Se2I42+. The difference in the structures of S2I42+ and Se2I42+ is related to the high strength of the S-S pi bond compared to the weak S-I sigma bond and the additional stabilization from increased delocalization of positive charge in the structure of S2I42+ compared to the structure of Se2I42+. The investigation of the E2X42+ series (E = S, Se, Te; X = Cl, Br, I) revealed that only S2I42+ adopts the highly np(pi)-np(pi) (n >= 3)-bonded structure, while all other dications favor the pi-bonded Se2I42+ structure. Theoretical bond order calculations for S2I42+ confirm the previously presented experimentally based bond orders for S-S (2.1-2.3) and I-I (1.3-1.5) bonds. The S-S bond is determined to hae the highest reported S-S bond order in an isolated compound and has a bond order that is either similar to or slightly less than the Si-Si bond order in the proposed triply bonded [(Me3Si)(2)CH](2)(Pr-i)SiSi=SiSi(Pr-i)[CH(SiMe3)(2)](2) depending on the definition of bond orders used.