  In this paper we classify all extremal and $s$-extremal binary self-dual
codes of length 38. There are exactly 2744 extremal $[38,19,8]$ self-dual
codes, two $s$-extremal $[38,19,6]$ codes, and 1730 $s$-extremal $[38,19,8]$
codes. We obtain our results from the use of a recursive algorithm used in the
recent classification of all extremal self-dual codes of length 36, and from a
generalization of this recursive algorithm for the shadow. The classification
of $s$-extremal $[38,19,6]$ codes permits to achieve the classification of all
$s$-extremal codes with d=6.
