Caradhras (in Khuzdul, the language of the Dwarves, Baranzibar) was one of the Mountains of Moria, the three mountains which the great Dwarf palace of Khazad-dûm was built under. Caradhras was also the site on Middle-earth where Mithril was found. It was here, though, that miners found Durin's Bane, the Balrog of Moria.
Caradhras was called the Cruel by the Dwarves and had long had a bad reputation. The Redhorn Pass (also called the Redhorn Gate, because it was the only pass through the Misty Mountains) was known to be treacherous.
In Peter Jackson's Lord of the Rings movie, when the Fellowship is trying to cross Caradhras, Saruman conjures a spell that causes violent snowstorms on the mountain. In the book, the Company generally blames the mountain itself.
The most important passes are the High Pass and the RedhornPass.
The Gap of Rohan was the valley (probably of the River Isen) between the southernmost peaks of the Misty Mountains and the northernmost of the White Mountains.
Carn Dûm, where the Witch-king of Angmar resided for several centuries in the Third Age, lay between a western spur of the northern extreme of the mountains, known as the Mountains of Angmar.