\begin{abstract}
A notion called {\em Herbrand saturation} is introduced, and is
shown to provide the model-theoretic analogue of a proof-theoretic
method, Herbrand analysis. This provides uniform and sometimes
simplified model-theoretic proofs of a number of important conservation
theorems, and helps clarify the relationship between semantic
and syntactic methods. A constructive, algebraic variation of
the new method is described, providing yet a third approach, which
is finitary but retains the semantic flavor of the model-theoretic
version.
\end{abstract}