  We put forward in this paper a uniform narrative that weaves together several
variants of Hrushovski-Kazhdan style integral, and describe how it can
facilitate the understanding of the Denef-Loeser motivic Milnor fiber and
closely related objects. Our study focuses on the so-called "nonarchimedean
Milnor fiber" that was introduced by Hrushovski and Loeser, and our thesis is
that it is a richer embodiment of the underlying philosophy of the Milnor
construction. The said narrative is first developed in the more natural complex
environment, and is then extended to the real one via descent. In the process
of doing so, we are able to provide more illuminating new proofs, free of
resolution of singularities, of a few pivotal results in the literature, both
complex and real. To begin with, the real motivic zeta function is shown to be
rational, which yields the real motivic Milnor fiber; this is an analogue of
the Hrushovski-Loeser construction. We also establish, in a much more intuitive
manner, a new Thom-Sebastiani formula, which can be specialized to the one
given by Guibert, Loeser, and Merle. Finally, applying $T$-convex integration
after descent, matching the Euler Characteristics of the topological Milnor
fiber and the motivic Milnor fiber becomes a matter of simple computation,
which is not only free of resolution of singularities as in the
Hrushovski-Loeser proof, but is also free of other sophisticated
algebro-geometric machineries.
