The part of a bicycle that connects the rear derailleur to the frame. Derailleur hangers and generally part of the frame if it's made of steel, and removeable if it's an aluminum/aluminium or carbon fibre frame. Titanium frames use either. The reason for this is that derailleur hangers run a constant risk of being bent by rocks, being dropped, etc. While a steel frame/hanger can be bent repeatedly without snapping and can be easily rewelded if necessary, an aluminum or carbon hanger would quickly fatigue and once it had snapped off the whole frame would need to be replaced.