  We approach the issue of exponentiation of soft gauge boson corrections to
scattering amplitudes from a path integral point of view. We show that if one
represents the amplitude as a first quantized path integral in a mixed
coordinate-momentum space representation, a charged particle interacting with a
soft gauge field is represented as a Wilson line for a semi-infinite line
segment, together with calculable fluctuations. Combining such line segments,
we show that exponentiation in an abelian field theory follows immediately from
standard path-integral combinatorics. In the non-abelian case, we consider
color singlet hard interactions with two outgoing external lines, and obtain a
new viewpoint for exponentiation in terms of ``webs'', with a closed form
solution for their corresponding color factors. We investigate and clarify the
structure of next-to-eikonal corrections.
