We review the role of the momentum of the electromagnetic (EM) fields Pe in several areas of modern physics. Pe represents the EM interaction in equations for matter and t waves propagation. As an application of wave propagation properties, a first order optical experiment which tests the speed of light in moving rarefied gases is presented. Within a classical context, the momentum Pe appears also in proposed tests of EM interactions involving open currents and angular momentum conservation laws.Moreover, Pe is the link to the unitary vision of the quantum effects of the Aharonov-Bohm (AB) type and, for several of these effects, the strength of Pe is evaluated. These effects provide a quantum approach to evaluate the limit of the photon mass mph. A new effect of the AB type, together with the scalar AB effect, provides the basis for table-top experiments which yield the limit mph = 9.4 × 10-52 g, a value that improves the results achieved with recent classical and quantum approaches.