Video communications have become increasingly popular, leading to increased IP data traffic. New video coding standards aim to reduce data usage. However, improved compression efficiency also increases the complexity of decoders, which significantly reduces battery lifetime on mobile devices. Additionally, video communications contribute to 1% of global greenhouse gas emissions. Thus, finding solutions for higher energy efficiency in video communications is crucial. This thesis addresses the challenge of reducing energy consumption in video communications by focusing on three main areas. First, it analyzes the compression and energy efficiency of the video coding standards AVC, VP9, HEVC, AV1, VVC, and AVM. The results indicate that AV1 is a sweet spot for optimized and reference software decoders. However, for hardware decoding, the energy demand of AV1 is increased by over 100% compared to VP9. The second area covers the modeling of the decoding energy demand. Linear and Gaussian process regression are evaluated, achieving an average estimation error of 1.38% for software decoding and of 1.79% for hardware decoding using software profiling. A framework is developed that predicts the energy demand of an unknown hardware decoder using information from existing software and hardware implementations with an error of less than 8% and a minimum error of 4.54%. This allows standardization to evaluate the expected energy demand of future hardware decoder implementations and reduce complexity if necessary. Finally, the thesis proposes a greedy strategy-based design space exploration for optimizing the energy demand of VVC software decoding. Furthermore, this strategy, is refined with alternative search strategies and cost functions, that reduces VVC energy demand by over 60%, with a bitrate increase of less than 30%. Thus, it is observed that the compression and energy efficiency of the proposed configuration for VVC is higher than for HEVC and AV1.