The list of σ-hole bonds is long and growing, encompassing both H-bonds and its closely related halogen, chalcogen, etc., sisters. These bonds rely on the asymmetric distribution of electron density, whose depletion along the extension of a covalent bond leaves a positive region of electrostatic potential from which these bonds derive their name. However, the density distributions of other molecules contain analogous positive regions that lie out of the molecular plane known as π-holes, which are likewise capable of engaging in noncovalent bonds. Quantum calculations are applied to study such π-hole bonds that involve linear molecules, whose positive region is a circular belt surrounding the molecule, rather than the more restricted area of a σ-hole. These bonds are examined in terms of their most fundamental elements arising from the spatial dispositions of their relevant molecular orbitals and the π-holes in both the total electron density and the electrostatic potential to which they lead. Systems examined comprise tetrel, chalcogen, aerogen, and triel bonds, as well as those involving group II elements, with atoms drawn from various rows of the Periodic Table. The π-hole bonds established by linear molecules tend to be weaker than those of comparable planar systems.