This paper studies energy-efficient resource allocation for mobile-edge computation offloading (MECO) in multiuser systems using time-division multiple access (TDMA) and orthogonal frequency-division multiple access (OFDMA). The goal is to minimize the weighted sum of mobile energy consumption while satisfying computation latency and cloud capacity constraints. For the TDMA system, the optimal resource allocation is formulated as a convex optimization problem, and it is shown that the optimal policy has a threshold-based structure based on an offloading priority function derived from channel gains and local computing energy consumption. Users above and below the threshold perform complete and minimum offloading, respectively. For the cloud with finite capacity, a sub-optimal algorithm is proposed to reduce computation complexity. For the OFDMA system, the optimal resource allocation is formulated as a non-convex mixed-integer problem, which is solved using a sub-optimal low-complexity algorithm by transforming the problem into its TDMA counterpart. The algorithm defines an average offloading priority function and shows that the resulting resource allocation has close-to-optimal performance. The paper also discusses the effects of finite cloud capacity and non-negligible computing time on the optimal resource allocation policy. The results show that the optimal policy has a threshold-based structure, and the offloading priority function is determined by factors such as channel gain, local computing energy, and fairness. The proposed algorithms are shown to have low complexity and close-to-optimal performance in simulations.This paper studies energy-efficient resource allocation for mobile-edge computation offloading (MECO) in multiuser systems using time-division multiple access (TDMA) and orthogonal frequency-division multiple access (OFDMA). The goal is to minimize the weighted sum of mobile energy consumption while satisfying computation latency and cloud capacity constraints. For the TDMA system, the optimal resource allocation is formulated as a convex optimization problem, and it is shown that the optimal policy has a threshold-based structure based on an offloading priority function derived from channel gains and local computing energy consumption. Users above and below the threshold perform complete and minimum offloading, respectively. For the cloud with finite capacity, a sub-optimal algorithm is proposed to reduce computation complexity. For the OFDMA system, the optimal resource allocation is formulated as a non-convex mixed-integer problem, which is solved using a sub-optimal low-complexity algorithm by transforming the problem into its TDMA counterpart. The algorithm defines an average offloading priority function and shows that the resulting resource allocation has close-to-optimal performance. The paper also discusses the effects of finite cloud capacity and non-negligible computing time on the optimal resource allocation policy. The results show that the optimal policy has a threshold-based structure, and the offloading priority function is determined by factors such as channel gain, local computing energy, and fairness. The proposed algorithms are shown to have low complexity and close-to-optimal performance in simulations.