  It is shown that, in a generic sense, and unlike what for electric point
charges, the Born--Infeld nonlinear electrodynamics excludes monopoles as
finite-energy magnetic point charges, thus spelling out an electromagnetic
asymmetry. Moreover, it is demonstrated, in a systematic way, that the
curvature singularities of finite-energy charged black holes in the context of
the Born--Infeld theory may effectively be relegated or in some cases removed
under a critical mass-energy condition, which has been employed successfully in
earlier concrete studies. Furthermore, it is illustrated through numerous
examples considered here that, when adapted to describe scalar-wave matters
known as k-essences, the Born--Infeld formalism provides a fertile ground for
cosmological applications, including achieving accelerated dark-energy
expansions and acquiring adequate field-theoretical realizations of the
equations of state of various cosmic fluid models.
