A detailed survey of approaches reducing energy consumption of core networks is presented in this paper. We consider a multilayer architecture, in which the optical layer can be realized either with a Wavelength Division Multiplexing (WDM) network or an Elastic Optical Network (EON). We focus on the design and operation stages, i.e., deciding which devices to install in the network during the former step, and choosing which devices to put into sleep mode during the latter one. A taxonomy for classifying the surveyed approaches is provided in order to compare the works covering energy efficiency in core networks (in terms of both optimal formulations and heuristic solutions). Moreover, our work provides a global view of the traffic assumptions, the topologies, and the power consumption models in the literature. The need of further investigations in this field clearly emerges. We envision future works targeting: (1) more effective standardization efforts to practically realize sleep modes; (2) the evaluation of the impact of sleep mode on the device lifetime; (3) the extensive adoption of new paradigms like Software Defined Networking (SDN) and EON; and (4) a radical improvement in the testbed implementations.