Fallen Angels
The Fallen Angels are renegade members of the Dark Angels Legion who turned on Lion El'Jonson during the Horus Heresy.
Okay, so after the Emperor found Caliban, Lion was made commander of the Dark Angels, and they began recruiting from Caliban's population, including taking on many of the Knights that served in the Order with Lion, including his friend and mentor Luther. According to conflicting accounts, most of the Terran Dark Angels were relegated to garrison duty on Caliban while Lion and the Calibanian Dark Angels went off and fought in the Great Crusade. This apparently caused no small amount of discontent among the garrisoned Angels, who were under the command of Luther. At some point after the Siege of Terra, Lion El'Jonson returned to Caliban, and the Dark Angels garrison opened fire on his fleet. Heading to their fortress-monastery, Lion fought Luther in single combat while the Dark Angels continued their orbital bombardment. Unfortunately, Caliban was never really tectonically stable, and the force of the bombardment caused the planet to break apart. The only thing to survive was the fortress-monastery. By the time Lion's loyalists got in, Luther was a gibbering wreck and Lion was nowhere to be seen. The garrisoned Dark Angels were apparently thrown through the Warp and scattered across the stars. Ever since, the Dark Angels have hunted for the Fallen Angels to restore their honor in the eyes of the Emperor.
However, things are a bit more complicated than that. Over the years, it has been shown that not all of the Fallen Angels are followers of Chaos, and some of the captured Fallen have claimed that Lion El'Jonson took his sweet time to get to Terra, implying that Lion El'Jonson was trying to wait and see who would win the civil war and side with the victor. Lion certainly had reason to be displeased with the Emperor (Horus suspected that he resented not being chosen as Warmaster, as he was the first Primarch). Whatever the truth is, only the Emperor knows, and he isn't talking. Mostly because his vocal cords have faded to dust, but that's beside the point.
Among the known Fallen Angels, the most famous is Cypher, whom Games Workshop hasn't given an update for in years.