The possibility of operating in remote environments using teleoperation systems has been considered widely in the control literature. This paper presents a review on the discrete-time teleoperation systems, including issues such as stability, passivity and time delays. Using discrete-time methods for a master-slave teleoperation system can simplify control implementation. Varieties of control schemes have been proposed for these systems and major concerns such as passivity, stability and transparency have been studied. Recently, unreliable communication networks affected by packet loss and variable transmission delays have been received much attention. Thus, it is worth considering discrete-time theories for bilateral teleoperation architectures, which are formulated on the same lines as the continuous-time systems. Despite the extensive amount of researches concerning continuous-time teleoperation systems, only a few papers have been published on the analysis and controller design for discrete bilateral forms. This paper takes into account the challenges for the discrete structure of bilateral teleoperation systems and notifies the recent contributions in this area. The effect of sampling time on the stability-transparency trade-off and the task performance is taken into consideration in this review. These studies can help to design guidelines to have better transparency and stable teleoperation systems.