The primary purpose of this paper is to give a complete classification of all finite simple groups with quasi-dihedral Sylow 2-subgroups. We shall prove that any such group must be isomorphic to one of the groups
L
3
(
q
)
{L_3}(q)
with
q
≡
−
1
(
mod
4
)
,
U
3
(
q
)
q \equiv - 1 \pmod 4,{U_3}(q)
with
q
≡
1
(
mod
4
)
q \equiv 1 \pmod 4
, or
M
11
{M_{11}}
. We shall also carry out a major portion of the corresponding classification of simple groups with Sylow 2-subgroups isomorphic to the wreath product of
Z
2
n
{Z_{{2^n}}}
and
Z
2
,
n
≧
2
{Z_2},n \geqq 2
.