TITLE: Classification of finite commutative rings
QUESTION [38 upvotes]: Is there a classification of finite commutative rings available? 
If not, what are the best structure theorem that are known at present? 
All I know is a result that every finite commutative ring is a direct product of local commutative rings (this is correct, right?) in some paper which computes the size of the general linear group over that ring.

REPLY [4 votes]: As always one should check out the OEIS for questions of this type. In this case see http://oeis.org/A027623