Low-cost, resource-constrained, maintenance-free, and energy-harvesting (EH) Internet of Things (IoT) devices, referred to as zero-energy devices (ZEDs), are rapidly attracting attention from industry and academia due to their myriad of applications. To date, such devices remain primarily unsupported by modern IoT connectivity solutions due to their intrinsic fabrication, hardware, deployment, and operation limitations, while lacking clarity on their key technical enablers and prospects. Herein, we address this by discussing the main characteristics and enabling technologies of ZEDs within the next generation of mobile networks, specifically focusing on unconventional EH sources, multi-source EH, power management, energy storage solutions, manufacturing material and practices, backscattering, and low-complexity receivers. Moreover, we highlight the need for lightweight and energy-aware computing, communication, and scheduling protocols, while discussing potential approaches related to TinyML, duty cycling, and infrastructure enablers like radio frequency wireless power transfer and wake-up protocols. Challenging aspects and open research directions are identified and discussed in all the cases. Finally, we showcase an experimental ZED proof-of-concept related to ambient cellular backscattering.