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This article reviews the state-of-the-art energy-efficient contention-based and scheduled-based medium access control (MAC) protocols for mobile sensor networks (MSNs) by first examining access schemes for wireless sensor networks (WSNs). Efficient and proper mobility handling in sensor networks provides a window of opportunity for new applications. Protocols, such as S-MAC, reduce energy consumption by putting nodes to sleep after losing to channel contention or to prevent idling. Sleeping is a common method for energy-efficient MAC protocols, but delay depends on sleep duration or frame time, and longer delays lead to higher packet lost rate when nodes are unsynchronized due to network mobility. MS-MAC extends S-MAC to include mobility-awareness by decreasing this sleep duration when mobility is detected. S-MAC with extended Kalman filter (EKF) reduces mobility-incurred losses by predicting the optimal data frame size for each transmission. MMAC utilizes a dynamic mobility-adaptive frame time to enhance TRAMA, a scheduled-based protocol, with mobility prediction. Likewise, G-MAC utilizes TDMA for cluster-based WSNs by combining the advantages of contention and contention-free MACs. Z-MAC also combines both methods but without clustering and allows time slot re-assignments during significant topology changes. All of the above MAC protocols are reviewed in detail.