They took them to the halls of the Elven King in his hall, a large cave at the edge of Mirkwood. The wood elves of Mirkwood, in The Hobbit, took the thirteen dwarves to their king's halls, where they were locked in by cellars and a magic gate.
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Context would be nice. However, by far the most famous work I can think of which has "wood elves" and "dwarves" is The Hobbit, in which the wood elves take the dwarves captive and bring them before their king Thranduil in "his halls" (the "halls" appear to be a sort of cavern system, though possibly that's only the cellars/dungeon in which the dwarves are kept until Bilbo rescues them).
The dwarves were captured and imprisoned by the elves in Mirkwood. Bilbo had to keep entering to form a plan and carry it out.
{| |- | In Chapter 9 of The Hobbit, the dwarves were captured by the elves. They had just escaped from the spiders in the previous chapter and were wandering around the forest. They were hungry and looking for food when they encountered the elves' feasting in the woods. After several failed attempts to 'crash the party' they were all captured, except Bilbo, who used his ring to escape. |}
I would think that he's referring to the imprisonment of the dwarves. The dungeon of the elves is underground.
Yes, in chapter 9 the dwarves (but not Bilbo) were imprisoned by the Wood-elves in Mirkwood forest.
Bilbo was enchanted by the opportunity to spend time with the elves. The Dwarves were suspicious of elves, always had been. the Dwarves were also mad at the Elves when they first entered Rivendell because the Elves were making fun of their beards.