Energy efficiency in fading channels in the presence of Quality of Service (QoS) constraints is studied. Effective capacity, which provides the maximum arrival rate that a wireless channel can sustain while satisfying statistical QoS 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. Through this analysis, energy requirements under QoS constraints are identified. The analysis is conducted under two assumptions: perfect channel side information (CSI) available only at the receiver and perfect CSI available at both the receiver and transmitter. In particular, it is shown in the low-power regime that the minimum bit energy required under 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 in the presence of QoS constraints 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, a characterization of the energy-bandwidth-delay tradeoff is provided. Comment: conference version appeared at Globecom 2008