  In this paper we establish the pathwise Taylor expansions for random fields
that are "regular" in the spirit of Dupire's path-derivatives \cite{Dupire}.
Our result is motivated by but extends the recent result of Buckdahn-Bulla-Ma
\cite{BBM}, when translated into the language of pathwise calculus. We show
that with such a language the pathwise Taylor expansion can be naturally
carried out to any order and for any dimension, and it coincides with the
existing results when reduced to these special settings. More importantly, the
expansion can be both "forward" and "backward" (i.e., the temporal increments
can be both positive and negative), and the remainder is estimated in a
pathwise manner. This result will be the main building block for our new notion
of viscosity solution to forward path-dependent PDEs corresponding to (forward)
stochastic PDEs in our accompanying paper \cite{BMZ}.
