This chapter proposes computation models of cathode-based electron guns along with assumptions that could be helpful for simplifying the computation. General problem of computation of the optimum structure of electron guns based on one-apex and multi-apex field-emission cathodes (the Almazov–Egorov model) is posed and solved. Then mathematical simulation of model triode electron-optical systems and methods of calculation of distribution of the electric field in forming and controlling systems based on a field-emission cathode and a small-aperture focusing diaphragm system are presented. The chapter presents a technique for calculating the optimum characteristics of the forming and controlling systems based on a field-emission cathode and a focusing diaphragm system and proceeds to proposing a computation model of electron trajectories in a field-emission cathode-based system is proposed.