Smoothing algorithms of various kinds have been around for several decades. However, some basic issues regarding the dynamical structure and the minimal dimension of the steady-state algorithm are still poorly understood. It seems fair to say that the subject has not yet reached a definitive form. In this paper, we derive a realization of minimal dimension of the optimal smoother for a signal admitting a state-space description of dimension n. It is shown that the dimension of the smoothing algorithm can vary from n to 2n, depending on the zero structure of the signal model. The dynamics (pole structure) of the steady-state smoother is also characterized explicitly and is related to the zero structure of the model. We use several recent ideas from stochastic realization theory. In particular, a minimal Markovian representation of the smoother is derived, which requires solving a nonsymmetric Wiener-Hopf factorization problem. In this way, the smoother is naturally expressed as the cascade of a whitening filter and a linear filter of least possible dimension, whose state space is a minimal Markovian subspace containing the smoothed estimate (x) over cap. This, among other aspects, affords a very simple calculation of the error covariance matrix of the smoother. A reduced-order two-filter implementation of the Mayne-Fraser type is obtained by solving a Riccati equation of reduced dimension, which is in general smaller than the dimension of the Riccati equations considered in the literature.