This paper presents a P+Damping control with gravity compensation for bilateral teleoperation systems, where the effects of time delays can be effectively addressed, and the motion synchronization and the transparency can be guaranteed. To further eliminate the direct measurement of human and environmental torques to save sensor installation space and reduce the hardware cost, a constructive unknown torque estimator is also proposed by tailoring the idea of unknown system dynamics estimator (USDE). This torque estimator with low-pass filter operations eliminates the requirement of joint acceleration and has only one tuning parameter, while it enables accurate estimation of external torques of both the local and remote manipulators. Nevertheless, this USDE-based torque estimator can be incorporated into the P+Damping control to simultaneously enhance transparency during the contact motion and ensure the synchronization of both position and velocity. Rigorous theoretical analyses are carried out to prove the stability and the claimed performances. Finally, the effectiveness of the proposed methods is demonstrated through simulation and experimental results.