How are organs matched to a recipient?

Organs are matched primarily through blood typing and body typing. The recipent has to have the same bloo type (ABO) as the donor or the recipients body will "reject" the organ - the body's own immune system will attack the organ as a foreign object. Also, you can't really give a 5'2", 115 lb person's kidney to a 6'5" 250 lb recipient. Size matters.