They are used where a simple low-cost circuit is needed which can oscillate at high frequencies (>50MHz[1]) by using overtones of a crystal, and also giving low phase noise.
[5] The more common modern form of the circuit uses just the emitter follower stage.
The emitter follower forms an amplifier with no phase shift.
This then produces a phase lead, which overall meets the Barkhausen criteria for self-oscillation.
[1][6] Both the better-known Pierce and Colpitts oscillator circuits may be considered as derivatives of the Butler.