They either provide a full-blown station to which the soldering iron is wired, powered straight by mains, or an iron powered by DC power. The Miniware TS1C takes up an interesting position here in ...
In addition to the soldering iron and 10 interchangeable tips, it included the hot-air rework gun, a voltmeter for checking electrical circuits, and a desoldering pump for removing liquid solder.
You can’t get a soldering iron under the part, of course. A hot plate provides heat from underneath. A gentle push from a hot air gun will push the solder balls over the melting edge.