Coulomb's Law is a fundamental principle describing the electric force between isolated charges, and represents the first quantitative law achieved in electromagnetism. The degree of confidence with which the law is experimentally known to hold was investigated after the law was put forth by Coulomb in 1785. The electrodynamics for massive particles suggests that a photon with a finite rest mass will cause a deviation from the inverse square law. So, modern interpretations of the possible deviation from Coulomb's inverse square law are usually associated with the non-zero photon mass. In this article, we first give a historical review of the foundation of Coulomb's inverse square law. Then, the experimental searches for validity of Coulomb's Law, particularly in its inverse square nature, are generally introduced. Based on Proca's equations, the unique simplest relativistic generalization of Maxwell's equations, the link between the deviation from Coulomb's Law and the upper limit on the photon rest mass based on the concentric-spheres apparatus established in the classical experiment of Cavendish is reviewed. Up to now, all the experiments show no evidence for a positive value, and the experimental result was customarily expressed as an upper limit on the deviation or on the photon rest mass. As a representative method with the double mission of testing of the validity of Coulomb's Law and of the photon rest mass, possible improvements for this kind of experiment are discussed.