  An NP-hard combinatorial optimization problem $\Pi$ is said to have an {\em
approximation threshold} if there is some $t$ such that the optimal value of
$\Pi$ can be approximated in polynomial time within a ratio of $t$, and it is
NP-hard to approximate it within a ratio better than $t$. We survey some of the
known approximation threshold results, and discuss the pattern that emerges
from the known results.
