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Maxwell electrodynamics and its modification are derived using quaternionic formulation. Starting from the quaternionic Maxwell's equation, all subsequent equations are derived in a very succinct way. The energy, momentum, and spin angular momentum conservation equations are defined for quaternionic electrodynamics. Using the modified electrodynamics, we formally derive London's equations of superconductivity without recourse to Newton's second law of motion. The modified electrodynamics allows a longitudinal scalar field to arise besides the transverse electromagnetic field. The influence of the scalar field is manifested in several phenomena we already encountered but we have incorporated such effects in the framework of Maxwell's electrodynamics. The non-uniformity and inhomogeneity of the medium, in which the electromagnetic field exists, affects the electromagnetic properties of the system in the way how the scalar field vary in space and time. Two different scenarios for quantum massive electrodynamics are proposed. One of the scenarios reduces to axion electrodynamics which further reduces to Maxwell–Proca massive boson electrodynamics. A quantum massive electrodynamic is studied and found not to alter the beauty of Maxwell's electrodynamics. Additional electric and magnetic charge densities are found to be induced with non-dissipative currents. [ABSTRACT FROM AUTHOR]