  In this paper, we study the well-posedness of the Forward-Backward Stochastic
Differential Equations (FBSDE) in a general non-Markovian framework. The main
purpose is to find a unified scheme which combines all existing methodology in
the literature, and to address some fundamental longstanding problems for
non-Markovian FBSDEs. An important device is a decoupling random field that is
regular (uniformly Lipschitz in its spatial variable). We show that the
regulariy of such decoupling field is closely related to the bounded solution
to an associated characteristic BSDE, a backward stochastic Riccati-type
equation with superlinear growth in both components $Y$ and $Z$. We establish
various sufficient conditions for the well-posedness of an ODE that dominates
the characteristic BSDE, which leads to the existence of the desired regular
decoupling random field, whence the solvability of the original FBSDE. A
synthetic analysis of the solvability is given, as a "User's Guide," for a
large class of FBSDEs that are not covered by the existing methods. Some of
them have important implications in applications.
