Information and Communication Technology (ICT) has been estimated to consume 10% of the total energy consumption in industrial countries. According to the latest measurements, this amount is rapidly increasing by 6% annually. With the evolved new business model in which Service Providers (SPs) are separated from Infrastructure Providers (InPs), Virtualized Network Environments (VNEs) have been regarded as a promising technology for flexibly utilizing shared communication network resources. VNEs also play a fundamental role toward virtualizing data centers. In this thesis, we suggest different feasible solutions to optimize the energy consumption in a VNE. In this regard, first, we review the corresponding literature in regard to the architecture of a VNE, its performance modelling, several power models, and also existing energy-saving solutions for VNEs. We approach the objective of optimizing the energy consumption in a VNE by defining and solving two main problems. The first problem optimizes the energy consumption in a VNE during the off-peak period. This is feasible by reconfiguring the mapping of already embedded virtual networks for the off-peak time. This is planned in two smaller and simpler sub-problems with increasing the complexity and higher energy-saving levels. Our solutions enable the providers to adjust the level of the reconfiguration and accordingly control the possible traffic disruptions. In the second problem, we propose a novel energy-efficient embedding method that maps heterogeneous MapReduce-based virtual networks onto a heterogeneous data center physical network, energy-wise. We introduce a new incast problem that specifically may happen in Virtualized Data Centers (VDCs). The proposed embedding process also controls the incast queueing delay.