Importantly, they have attacked units of Saddam's tough, loyal soldiers - the Republican Guards - to make sure they aren't a threat to them as they move closer to the capital.
The guards were bombarded at Karbala and Kut, close to Baghdad.
Tough time ahead
US marines say they have captured a key bridge at the city of Kut in the east, which gives them free access into the capital.
But US officials have warned they are not expecting to "drive into Baghdad and suddenly seize it".
They have also said there is some tough fighting ahead.