Currently controlling the Iron Throne is basically House Lannister. The previous House was House Targaryen. In this week's releases for the A Song of Ice and Fire: Tabletop Miniatures Game, those two factions are getting reinforcements out on the battlefield.
From the article:
Two of the most recent Houses to occupy the Iron Throne are the factions getting new units in the latest set of releases for the A Song of Ice and Fire: Tabletop Miniatures Game. House Targaryen held the crown until Robert’s Rebellion. Though King Robert’s eldest son, Joffrey, now claims the throne, it’s really House Lannister, his mother’s powerful noble house, that truly rules from King’s Landing. Let’s take a look at what new surprises House Targaryen and Lannister will bring to the field.