In molecular simulations, it is essential to properly calculate the electrostatic interactions of particles in the physical system of interest. Here we consider a method called the non-Ewald method, which does not rely on the standard Ewald method with periodic boundary conditions, but instead relies on the cuto¤-based techniques. We focus on the physicochemical and mathematical conceptual aspects of the method in order to gain a deeper understanding of the simulation methodology.In particular, we take into account the reaction …eld (RF) method, the isotropic periodic sum (IPS) method, and the zero-multipole summation method (ZMM). These cuto¤-based methods are based on di¤erent physical ideas and are completely distinguishable in their underlying concepts. The RF and IPS methods are "additive" methods that incorporate information outside the cuto¤ region, via dielectric medium and isotropic boundary condition, respectively. In contrast, the ZMM is a "subtraction" method that tries to remove the arti…cial e¤ects, generated near the boundary, from the cuto¤ sphere. Nonetheless, we …nd physical and/or mathematical similarities between these methods. In particular, the modi…ed RF method can be derived by the principle of neutralization utilized in the ZMM, and we also found a direct relationship between IPS and ZMM.