This paper presents model-based predictive controllers that achieve a high level of transparency while maintaining stability in bilateral teleoperation under known constant or variable time delay. This goal is accomplished by utilizing available information on system model and time delay within an adaptive predictive control framework. The performance objectives are delay-free position tracking between the master and slave and the establishment of virtual mass-damper tool impedance between the user and environment. The controllers adapt to parameter changes in the user, environment as well as the master and slave dynamics. Delay reduction is accomplished based on a state observer and estimates of the system parameters. Using the delay-reduced dynamics, an adaptive output regulation problem is formulated and solved to obtain the control laws. A Lyapunov analysis of the performance and stability of the resulting system is presented. The proposed controllers are evaluated experimentally under constant and variable delay conditions.