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This dissertation deals with various issues in wireless communications under statistical quality of service (QoS) constraints. Effective capacity, which provides the maximum constant arrival rate that a wireless channel can sustain while satisfying statistical QoS constraints, is adopted as the performance metric. Energy efficiency of point-to-point links is first studied by characterizing the spectral efficiency-bit energy tradeoff in the low-power and wideband regimes. Different transmission strategies (with variable or fixed rate) and power policies are studied. Then, the effective capacity region for fading multiple-access channels (MAC) is investigated for different transmission strategies: Superposition coding with successive decoding and time division multiple acess (TDMA). With fixed power, it is shown that varying the decoding order with respect to the channel states can significantly increase the achievable throughput region. In the two-user case, the optimal decoding strategy is determined for the scenario in which the users have the same QoS constraints. The optimal power allocation policies for any partition of the channel state space are identified. With the characterization of effective capacity regions, the energy efficiency of MAC is investigated by quantizing the minimum bit energy and wideband slope regions for different transmission strategies. In addition, the throughput for the two-hop wireless communication links with individual QoS constraints at the source and relay nodes is determined as a function of the QoS parameters and signal-to-noise ratios at the source and relay, and the fading distributions of the links. The analysis is performed for both full-duplex and half-duplex relaying. Finally, the throughput with finite blocklength channel codes is analyzed for variable-rate and fixed-rate transmissions in single-user settings. The optimum error probability for variable-rate transmission and the optimum coding rate for fixed-rate transmission are shown to be unique.