An antifriction bearing (A) for accommodating rotation about an axis (X) comprises an inner race (2) having a raceway (12), an outer race (4) having a raceway (22), rolling elements (6) positioned between the inner and outer races (2, 4) and contacting the raceways (12, 22) of those races (2, 4) so that when relative rotation occurs between the races (2, 4) the rolling elements (6) roll along the raceways (12, 22), a cage (8) positioned between the inner and outer races (2, 4) and having pockets (40) in which the rolling elements (6) are received with the cage (8) being rotatable between the races (2, 4) as the rolling elements (6) roll along the raceways (12, 22), the outer race (4) having a power transmitting coil (50) and a receiver (60), the cage (8) having a power receiving coil (52), a sensing unit (D) for sensing a condition of the bearing (A), and a transmitter (54) for sending a signal indicative of the sensed condition of the bearing (A) to the receiver (60).