Variable and potential plasma applications in aerospace engineering are exemplified by ion thrusters, flow control by plasma actuator, enhanced ignition and combustion stability. The operational environments span a range from the rarefied to continuum gasdynamic regimes; however, the ionization process in practical applications is mostly by electron impact. The fundamental ionization mechanisms by electron impact consist of electron secondary mission and the cascading process. In an alternating electric field, unsteady and random micro discharges or streamers are always presented; therefore the discharge physics imposes a formidable challenge for incisive understanding. Meanwhile, the ionized species constitute hundreds of metastable chemical species; under this circumstance the physics-based modeling for analyzing the inhomogeneous medium becomes necessary. A summary of the physics-based modeling for electron impact ionization from the Boltzmann distribution equation to the inelastic particle kinetics formulation is delineated.