The advancements in smart power grid and the advocation of "green communications" have inspired the wireless communication networks to harness energy from ambient environments and operate in an energy-efficient manner for economic and ecological benefits. This article presents a contemporary review of recent breakthroughs on the utilization, redistribution, trading and planning of energy harvested in future wireless networks interoperating with smart grids. This article starts with classical models of renewable energy harvesting technologies. We embark on constrained operation and optimization of different energy harvesting wireless systems, such as point-to-point, multipoint-to-point, multipoint-to-multipoint, multi-hop, and multi-cell systems. We also review wireless power and information transfer technologies which provide a special implementation of energy harvesting wireless communications. A significant part of the article is devoted to the redistribution of redundant (unused) energy harvested within cellular networks, the energy planning under dynamic pricing when smart grids are in place, and two-way energy trading between cellular networks and smart grids. Applications of different optimization tools, such as convex optimization, Lagrangian dual-based method, subgradient method, and Lyapunov-based online optimization, are compared. This article also collates the potential applications of energy harvesting techniques in emerging (or upcoming) 5G/B5G communication systems. It is revealed that an effective redistribution and two-way trading of energy can significantly reduce the electricity bills of wireless service providers and decrease the consumption of brown energy. A list of interesting research directions are provided, requiring further investigation.Index Terms-5G/B5G communication networks, energy har-). The first two authors contributed equally to this work. vesting, smart grid, energy redistribution and trading, optimization techniques. arXiv:1912.13203v1 [eess.SY] 31 Dec 2019 EH and smart gridpowered wireless networks Types and models for RES (Sec. II) Smart grid-powered wireless networks (Sec. VIII) Wireless power and information transfer (Sec. VII) 5G/B5G applications of EH and smart gridpowered wireless networks (Sec. XI) Energy redistribution Energy planning under dynamic pricing (Sec. IX) Two-way energy trading and cooperation (Sec. X) EH-based wireless networks Point-to-point link (Sec. III) Multipoint-to-point system (Sec. IV) Multipoint-to-multipoint system (Sec. V) Multi-hop link (Sec. VI) Lessons learnt and future directions (Sec. XII) Fig. 1. The main structure of this article. from the aspects of network deployment, energy/spectrum efficiency, and delay/bandwidth versus power. Featuring energyharvesting wireless networks, beamforming techniques are reviewed in [22]. Energy scheduling, optimization, and application are presented in [23]. Circuit design, hardware implementation, EH techniques, and communication protocols are reviewed in [24]-[27] with specific emphases on radio frequen...