The interactions between a wide variety of molecules having σ-holes or π-holes and several nitrogen bases have been analyzed computationally. The σ- and π-hole atoms span groups III-VII of the periodic table. The interaction energies range from quite weak, typical of non-covalent bonding, to unusually strong: from -4.6 to -22.0 kcal/mol for σ-hole bonding and from -4.0 to -42.4 kcal/mol for π-hole bonding. The markedly greater strengths of some bonds does not imply that any new factors or types of bonding are involved; they simply reflect higher degrees of the polarization that is part of any Coulombic interaction. To explain the stronger bonding, this polarization must be explicitly taken into account. We show that the interaction energies can be related quite well to (a) the maximum positive electrostatic potentials associated with the σ- or π-holes on their molecular surfaces, (b) the polarizabilities of the nitrogen bases, and especially (c) the polarizing electric fields of the σ- or π-hole molecules at the positions of the nitrogens.