The Blue Mountains (also called Ered Luin) are a range of blue mountains to the west of Eriador and The Shire. They were home to Dwarves, namely the Firebeards and Broadbeams in the First Age, and refugees of Erebor in the Late Third Age.
In the First Age, the Blue Mountains were an unbroken line separating Eriador from Beleriand. The Blue Mountains were ruined during the War of Wrath at the end of the First Age, and in the south central end of the range the sea broke through. On the western side a small section of Lindon remained, and here the retreating Elves built the kingdom of Lindon
Sometime during the Years of the Trees two Dwarven Fathers awoke under Mount Dolmed and founded the two westernmost houses of the Dwarves (the Firebeards and Broadbeams). They subsequently built two great city-states, Nogrod and Belegost. A Dwarven Road was built through Eriador to connect Belegost and Nogrod with the Kingdom of Durin's Folk in Moria.
The Dwarven cities of Nogrod and Belegost were also ruined when the mountains were broken, causing most of the Dwarves to migrate east to Khazad-dûm, leaving a remnant behind. However, there remained some Dwarves on the eastern side of the Blue Mountains in days afterwards, especially in the parts south of the Gulf of Lhun where they have mines that are still in use. In TA 1974, fleeing the fall of Fornost Erain, Arvedui briefly hid in old dwarven mines in the far north of the Blue Mountains.
It also became the new home for many of Durin's Folk who were exiled from their halls in Erebor by Smaug the Dragon who had driven them out. After the Battle of Moria, Thorin established his throne in the Southern range beyond the Shire and many of the wandering Longbeards joined him in his halls and they became prosperous in a fashion. Some local Dwarves joined their ranks, and Bombur, Bofur and Bifur hailed from these, probably from the Broadbeams. Erebor was retaken from Smaug by Thorin and company in T.A. 2941, and it can be assumed most if not all of Durin's folk relocated there, although Dwarves continued to cross the Shire to mine the Blue Mountains.