In this paper, existing results regarding the fundamental limits of simultaneous energy and information transmission in wireless networks are reviewed. In point-to-point channels, the fundamental limits on the information rate given a minimum energy rate constraint are fully characterized by the notion of information-energy capacity function introduced by Varshney in 2008. In a centralized multi-user channel, the fundamental limits on the information rates given a minimum energy rate constraint are described by the notion of information- energy capacity region introduced by Fouladgar and Simeone in 2012. Alternatively, in a decentralized multi-user channel, the authors have recently introduced the notion of information- energy Nash region to describe these fundamental limits. All these fundamental limits reveal the intrinsic trade-off between the two conflicting tasks of information and energy transmission.