Having "the blues" after childbirth is so common it's considered normal. However, 10% to 25% of women experience a major depression within the first 6 months after childbirth. The abrupt drop in estrogen after delivery seems like the obvious culprit -- but this link has never been proven.
Postpartum depression is treated like any other depression -- with antidepressants, therapy, or both. Some preparations of estrogen do show promise as a potential add-on to these established treatments.