Blue MountainsBlue Mountains - So while Smaug was residing in Erebor and the Orcs were firmly in control of Moria, the Dwarves made a home of the Blue Mountains for a time.  Thráin, son of Thrór led them there after the War of the Dwarves and Orcs.  Called Ered Luin in the Eldar Days.


"So it was that after Azanulbizar the dwarves dispersed again...So Thráin and Thorin with what remained of their following (among whom were Balin and Gloin) returned to Dunland, and soon afterwards they removed and wandered in Eriador, until at last they made a home in exile in the east of the Ered Luin beyond the Lune." ~The Return of the King (Appendix A)


The events between the takeover of Erebor by Smaug and the death of Thráin are summed up as follows:


"The Dwarves Thrór and his son Thráin (together with Thráin's son Thorin, afterwards called Oakenshield) escaped from the Lonely Mountain (Erebor) by a secret door when the dragon Smaug descended upon it.  Thrór returned to Moria, after giving to Thráin the last of the Seven Rings of the Dwarves, and was killed there by the Orc Azog, who branded his name on Thrór's brow.  It was this that led to the War of the Dwarves and the Orcs, which ended in the great Battle of Azanulbizar (Nanduhirion) before the East-gate of Moria in the year 2799.  Afterwards Thráin and Thorin Oakenshield dwelt in Ered Luin, but in the year 2841 Thráin set out from there to return to the Lonely Mountain.  While wandering in the lands east of Anduin he was captured and imprisoned in Dol Guldur, where the ring was taken from him.  In 2850 Gandalf entered Dol Guldur and discovered that its master was indeed Sauron; and there he came upon Thráin before he died." ~Unfinished Tales (The Quest of Erebor)