he vacuum of quantum electrodynamics is unstable against the formation of many-body states in the presence of an external electric field, manifesting itself as the creation of electron-positron pairs (Schwinger effect). This effect has been a long-standing but still unobserved prediction as the generation of the required field strengths has not been feasible so far. However, due to the advent of a new generation of high-intensity laser systems such as the European XFEL or the Extreme Light Infrastructure (ELI), this effect might eventually become observable within the next decades. Previous investigations of the Schwinger effect led to a good understanding of the general mechanisms behind the pair creation process, however, realistic electric fields as they might be present in upcoming high-intensity laser experiments have not been fully considered yet. Actually, it was only recently that it became possible to study the Schwinger effect in realistic electric fields showing both temporal and spatial variations owing to the theoretical progress as well as the rapid development of computer technology. Based on the equal-time Wigner formalism, various aspects of the Schwinger effect in such inhomogeneous electric fields are investigated in this thesis. Regarding the Schwinger effect in time-dependent electric fields, analytic expressions for the equal-time Wigner function in the presence of a static as well as a pulsed electric field are derived. Moreover, the pair creation process in the presence of a pulsed electric field with sub-cycle structure, which acts as a model for a realistic laser pulse, is examined. Finally, an ab initio simulation of the Schwinger effect in a simple space- and time-dependent electric field is performed for the first time, allowing for the calculation of the time evolution of various observables like the charge density, the particle number density or the number of created particles.