  We present a streamlined account of recent developments in the stability
theory for planar viscous shock waves, with an emphasis on applications to
physical models with ``real,'' or partial viscosity. The main result is the
establishment of necessary, or ``weak'', and sufficient, or ``strong'',
conditions for nonlinear stability analogous to those established by Majda
[Ma.1--3] in the inviscid case but (generically) separated by a codimension-one
set in parameter space rather than an open set as in the inviscid case. The
importance of codimension one is that transition between nonlinear stability
and instability is thereby determined, lying on the boundary set between the
open regions of strong stability and strong instability (the latter defined as
failure of weak stability). Strong stability holds always for small-amplitude
shocks of classical ``Lax'' type [PZ.1--2, FreS]; for large-amplitude shocks,
however, strong instability may occur [ZS, Z.3].
