  A saturated fusion system over a finite $p$-group $S$ is a category whose
objects are the subgroups of $S$ and whose morphisms are injective
homomorphisms between the subgroups satisfying certain axioms. A fusion system
over $S$ is realized by a finite group $G$ if $S$ is a Sylow $p$-subgroup of
$G$ and morphisms in the category are those induced by conjugation in $G$. One
recurrent question in this subject is to find criteria as to whether a given
saturated fusion system is realizable or not.
  One main result in this paper is that a saturated fusion system is realizable
if all of its components (in the sense of Aschbacher) are realizable. Another
result is that all realizable fusion systems are tame: a finer condition on
realizable fusion systems that involves describing automorphisms of a fusion
system in terms of those of some group that realizes it. Stated in this way,
these results depend on the classification of finite simple groups, but we also
give more precise formulations whose proof is independent of the
classification.
