Max Born and Leopold Infeld reformulated Maxwell electrodynamics in the presence of a maximal electrostatic field which leads to a finite self-energy for an electron. In 1983, E. Iacopini and E. Zavattini introduced a (p,tau) -two-parameter modification of Born-Infeld electrodynamics, in which the self-energy of a point-like charge becomes finite for p<1 (Nuovo Cimento B 78, 38 (1983)). In this paper, a detailed review of Born-Infeld electrodynamics and its modifications are presented.
