Recent research in Future Wireless Networks (FWN)s have primarily focused on improving spectral and energy efficiency, emphasizing less on reducing power consumption. Studies on current Fifth Generation (5G) system deployment have shown that they consume more power than their predecessors, thus highlighting the need for significant efforts to minimize their carbon footprint. This work specifically focuses on the power consumption considerations, starting from the transceiver design and extending to an entire network design that can accomplish future Net Zero (NZ) targets. It is envisioned that smart grid-controlled renewable-powered systems, combined with artificial intelligence (AI) algorithms and Zero Touch (ZT) solutions, will play a central role to achieve Net Zero - Zero Touch Future Wireless Networks (NZ- ZT-FWNs). This work thoroughly investigates the recent research efforts, limitations of existing approaches and identifies key research areas for realizing NZ-ZT-FWNs.