With the rapid development of wireless communication technology in the last decade, the spectrum resource becomes a bottleneck to wireless communication. Meanwhile, recent spectrum analysis reports show that a large number of licensed spectrum are under utilized in either spatial do main or either time domain. In this context, cognitive radio (CR) technology has been proposed as a promising technology to resolve the spectrum under utilization problem by allowing unlicensed users (SUs, as well as CR users) to access to the licensed spectrum opportunistically.Cognitive radio networks (CRN), where CR is typically equipped with powerful computation, is capable of detecting surrounding radio environment and adapting its operating parameters (i.e., transmission power, channel, modulation). Consequently, CRN has been generally acknowledged as a potential paradigm to effective utilize spectrum. However, one of the main challenges in CRN is high energy consumption due to two reasons discussed as below. First, CRN may be restricted by their implementation terminals, especially in battery-powered terminals. On the other hand, in contrast to traditional wireless networks, CRN needs more energy for performing extra operations, such as spectrum sensing. In this thesis, we address energy efficiency problem of CRN from two perspectives: (1) resource allocation and (2) spectrum sensing.In the resource allocation perspectives, firstly, we proposed a multi-radio access technology (Multi-RAT) enabled heterogeneous cognitive radio networks (HeCRNets) model, in which multiple heterogeneous primary networks (PNets) are coexistent. Then, we focus on energy efficiency problem of CR users locate in the overlapping region of heterogeneous primary networks. The genetic algorithm (GA) is introduced to find an optimal energy efficiency resource allocation solution includes power and bandwidth allocation. In order to overcome the shortage of GA, we propose a two-tier crossover genetic algorithm based search schemes (TTCS) to expand search space for an optimal solution.In the spectrum sensing perspective, we focus on energy-efficient local spectrum sensing (LSS) and energy-efficient cooperative spectrum sensing (CSS), respectively. In LSS, we introduce the Markov model (MM) to analysis the relationship between spectrum sensing time interval and spectrum sensing results. On this basis, we propose a predictable spectrum sensing time interval strategy, where CR users can adaptively adjust begging of next spectrum sensing time based on the current spectrum sensing results. In CSS, we propose a correlation of spectrum sensing results based cluster scheme, where consist of pruning stage, selecting stage, and clustering stage.