QED predictions have been very well tested in the high-energy, low-intensity regime using particle accelerators and spectroscopic experiments. In the presence of strong background fields, QED acquires novel features and one enters an interesting field of physics: strong-field or high-intensity QED. However, many QED processes remain untested in the regime of low photon energy but high photon intensity, and only a few experiments has been made in this regime. The QED quantum vacuum made up of virtual pairs, when exposed to intense light or strong field, effectively behaves as a birefringent medium. This effect which is a manifestation of nonlinear photon-photon scattering is due to nonlinear interactions introduced into the linear Maxwell equation. Detection of vacuum nonlinear electrodynamics effects would be of profound importance for our understanding of the physical vacuum, and therefore possible tests of such effects are of great interest to a wide community of physicists. In this thesis we begin by reviewing prescription of the polarization by Stokes parameters and the evolution in time obeying the quantum Boltzmann equation. Based on this formalism, we consider the polarization effects caused by the photon-photon interaction in laser experiments, when a laser beam propagates through a constant magnetic field or collides with another laser beam. We solved the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian for both time-dependent and static background fields to explore the time evolution of Stokes parameters Q, U, and V. Our results confirm previous studies in the presence of the constant background field and predict some new effects in the case of time-dependent background fields. These new effects are at the limit of the accuracy that can now be obtainable with high-precision experiments. Astrophysics already offer environments where QED processes may be influential. For astrophysical purposes we explore the impact of nonlinear QED interactions on the polarization evolution of photons propagating through the magnetized vacuum of a pulsar. We find that linearly polarized X-ray photons propagating outward in the magnetosphere of a rotating neutron star can acquire high values for the circular polarization parameter. Meanwhile, it is shown that the polarization characteristics of photons besides photon energy depend strongly on parameters of the pulsars such as magnetic field strength, inclination angle and rotational period. Our results are clear predictions of QED vacuum polarization effects in the near vicinity of magnetic stars which can be tested with the upcoming X-ray polarimetric observations. Besides, we focus on Gamma-Ray Bursts (GRBs) as the most luminous objects in the universe. Since a charged black hole can produce enough energy to power a GR by means of QED pair production and subsequent expansion and annihilation of the plasma, It is possible to trace out Strong-field QED processes by GRB spectral analysis. Here we concentrate on the observational data from different satellites in order to extracting the physical information from spectrums and light curves which are two main observables. Following the standard data reduction procedures and spectral model fitting methods, we find thermal components in the X-ray flares of 13 sources of Binary-driven Hypernovae (BdHN). Thermal components are clear signatures of the presence of electron-positron plasma in thermal equilibrium. Furthermore we consider a universal power-law behavior exhibited by the late X-ray emission of 161 sources of BdHN, by introducing emission angles for each source.