  A fully consistent classical relativistic electrodynamics with spinless point
charges is constructed. The classical evolution of the electromagnetic fields
is governed by the nonlinear Maxwell--Born--Infeld field equations, the
classical evolution of the point charges by a many-body Hamilton--Jacobi law of
motion. The Pauli principle for bosons can be incorporated in the classical
Hamilton--Jacobi formalism. The Cauchy problem is explained and illustrated
with examples. The question of charge-free field solitons is addressed also and
it is shown that if they exist, their peak field strengths must be enormous.
The value The value of Born's constant is shown to be a subtle open issue.
