The centrifugal pendulum vibration absorber (CPVA) is a rotating mechanical device that counteracts order-specific torque fluctuations in a rotating system by the reciprocating motion of multiple mass absorbers on a predetermined path. The downsizing of automotive engines and supercharging technologies have promoted the research and application of CPVA in drivelines. The development of CPVA is reviewed, a variety of typical CPVA structural features are described such as unifilar type, parallel bifilar type, trapezoidal bifilar type, roller type and synchronous type. The non-linear characteristics of the CPVA such as jumps and asynchronous response are discussed in detail. Mathematical methods for establishing and solving the equations of motion, the excitation of the CPVA by the gravity field, modal property analysis, the effect of the type of damping between the damper and the rotor, and the effect of manufacturing deviations on system performance are discussed. The main research results of CPVA are summarized, current research hotspots and difficulties are summarized, future development directions are proposed, and suggestions are made for future research on powertrain electrification.