In this chapter, we dive deeper to understand how the ion–ion interaction is mathematically treated in the elegant Debye–Hückel model. A step-by-step derivation allows us to see how a complicated multi-body problem is simplified by the concept of an “ionic cloud”, and how the atomic picture of ion–ion interaction is verified by macroscopic properties. Links of the Debye–Hückel model to modern electrolytes in the super-concentration regime are briefly discussed.