The forest that the Dwarves cross in J.R.R. Tolkien’s The Hobbit is Mirkwood.
Mirkwood lies east of the Anduin and north of the lands around the Lonely Mountain. During the quest, Thorin’s company enters the forest after Gandalf leaves them, and they struggle to follow the Elven path through its dangerous wilderness.
The travelers face giant spiders and are captured by the Elves of the Woodland Realm. Their imprisonment ends when Bilbo uses the Ring and a concealed barrel escape to help the company reach Lake-town.
Tolkien’s Mirkwood was formerly called Greenwood the Great. Its character changes after Sauron establishes the fortress of Dol Guldur in the southern part of the forest, leading to the later name ‘Mirkwood.’