Hammerfell has come to the aid of Skyrim, sending some soldiers to boost the relatively pitiful numbers of Skyrim. Hammerfell has fallen victim to the Thalmor's assaults as well, though they were doing better than Skyrim. The only reason that they haven't burned it yet is because the College cast spells to keep it from burning.
The College of Winterhold has started to accept refugees that are afraid of the Thalmor breaking down the wall.
Dragon Bridge has not seen violence yet because they took the action to knock down the Dragon Bridge itself. Some of the villagers from Ivarstead have sought refuge on High Hrothgar. The previously unwalled cities and towns, such as Winterhold and Rorikstead, have built makeshift walls. There is an active assault on Riverwood, Ivarstead, Markarth, Rorikstead, Windhelm, and Winterhold. Falkreath fell next, and then the ruins of Helgen.
They took Riften relatively easily, and then Shor's Stone. The Thalmor launched their campaign on Skyrim on the tenth of Heartfire. Cyrodiil fell easily, and soon Elsweyr, Black Marsh, Morrowind, and High Rock followed. After the civil war in Skyrim (which the Stormcloaks won), the Thalmor decided that it was the perfect time to take back Tamriel, which, in their eyes, was theirs to begin with, and Talos stole their land to begin with. The setting is a single year after the events of Skyrim.