An acetabular cup remover comprising: a head dimensioned to seat in an acetabular cup; a shaft that extends proximally from the head, the shaft having a distal end and a longitudinal axis that extends distally to proximally through the shaft; a blade that is pivotally connected to said shaft, said blade being shaped and being connected to said shaft so as to be selectively pivotable into positions that are located forward of the acetabular cup; an actuator assembly (332, 418, 468, 502) moveably mounted to said shaft that is connected to the blade for controlling the extent to which the blade is pivoted, the actuator assembly including a handle that is moveably connected to said shaft that is manually displaced to pivot the blade; and a coupling assembly for connecting the blade to a driver so that rotational or oscillatory actuation of a component associated with the driver is transferred to the blade so as to cause oscillatory motion of the blade in arc around the acetabular cup, characterized in that: the blade, in addition to being pivotally connected to the shaft, is connected to the shaft to rotate around the longitudinal axis through the shaft; and an indexing assembly is attached to said blade to cause the blade to, in addition to engaging in pivotal motion relative to said shaft and oscillatory motion in an arc around the acetabular cup, engage in rotational motion about the longitudinal axis of the shaft upon actuation of the indexing assembly, wherein the handle is part of the indexing assembly and is further connected to said blade to rotate the blade around the shaft longitudinal axis to set a rotational orientation of the blade relative to the acetabular cup. a head dimensioned to seat in an acetabular cup; a shaft that extends proximally from the head, the shaft having a distal end and a longitudinal axis that extends distally to proximally through the shaft; a blade that is pivotally connected to said shaft, said blade being shaped and being connected to said shaft so as to be selectively pivotable into positions that are located forward of the acetabular cup; an actuator assembly (332, 418, 468, 502) moveably mounted to said shaft that is connected to the blade for controlling the extent to which the blade is pivoted, the actuator assembly including a handle that is moveably connected to said shaft that is manually displaced to pivot the blade; and a coupling assembly for connecting the blade to a driver so that rotational or oscillatory actuation of a component associated with the driver is transferred to the blade so as to cause oscillatory motion of the blade in arc around the acetabular cup, characterized in that: the blade, in addition to being pivotally connected to the shaft, is connected to the shaft to rotate around the longitudinal axis through the shaft; and an indexing assembly is attached to said blade to cause the blade to, in addition to engaging in pivotal motion relative to said shaft and oscillatory motion in an arc around the acetabular cup, engage in rotational motion about the longitudinal axis of the shaft upon actuation of the indexing assembly, wherein the handle is part of the indexing assembly and is further connected to said blade to rotate the blade around the shaft longitudinal axis to set a rotational orientation of the blade relative to the acetabular cup. the blade, in addition to being pivotally connected to the shaft, is connected to the shaft to rotate around the longitudinal axis through the shaft; and an indexing assembly is attached to said blade to cause the blade to, in addition to engaging in pivotal motion relative to said shaft and oscillatory motion in an arc around the acetabular cup, engage in rotational motion about the longitudinal axis of the shaft upon actuation of the indexing assembly, wherein the handle is part of the indexing assembly and is further connected to said blade to rotate the blade around the shaft longitudinal axis to set a rotational orientation of the blade relative to the acetabular cup.