Energy efficiency in fading channels in the presence of QoS constraints is studied. Effective capacity, which provides the maximum constant arrival rate that a given process can support while satisfying statistical delay constraints, is considered. Spectral efficiency-bit energy tradeoff is analyzed in the low-power and wideband regimes by employing the effective capacity formulation, rather than the Shannon capacity, and energy requirements under QoS constraints are identified. The analysis is conducted for the case in which perfect channel side information (CSI) is available at the receiver and also for the case in which perfect CSI is available at both the receiver and transmitter. In particular, it is shown in the low-power regime that the minimum bit energy required in the presence of QoS constraints is the same as that attained when there are no such limitations. However, this performance is achieved as the transmitted power vanishes. Through the wideband slope analysis, the increased energy requirements at low but nonzero power levels are determined. A similar analysis is also conducted in the wideband regime, and minimum bit energy and wideband slope expressions are obtained. In this regime, the required bit energy levels are found to be strictly greater than those achieved when Shannon capacity is considered. Overall, an energy-delay tradeoff is characterized.