Answers:
Hemolytic Disease of the Newborn.
An Rh+ fetus is developing in an Rh- mother who has been sensitized the the Rhesis factor (Rh) before hand through a previous pregnancy or blood transfusion.
The mother's Rh+ antibodies (these are antibodies that attack cells with the Rh factor on them) cross the placenta and attack the fetus, effectively lysing (killing) its blood cells.
When dealing with the Rhesis factor, HDN is generally fatal to the infant. To combat this, the infants can have all of their blood replaced while in gestation, or the mother can be given a shot that desensitizes her to the Rhesis factor at around 27 weeks or so, or immediately after her first Rh+ pregnancy. The latter is generally preferred as it involves fewer complications to future pregnancies.
There are other cases of HDN, that involve different blood types. In fact, most babies are born to some degree with differing blood types due to the 600 or so different antigens located on the RBC surfaces. Treatment for this is just good old fashioned sunlight, as it further breaks down the RBC's that have been lysed.