The desire for battery longevity and ubiquitous wireless charging of mobile devices is driving researchers to explore divergent strategies to extract and harness energy from ambient radio frequency (RF) signals. Different rectenna designs to convert or rectify energy from electromagnetic (EM) signals into direct current (DC) have been explored for wireless power transfer (WPT) and wireless energy harvesting (WEH). However, these rectennas are characterized by low energy capturing and RF-to-DC conversion deficiencies, complex rectifier design, and bulky size. Recently, man-made materials such as metasurfaces with unique EM properties have emerged to address these limitations of existing rectenna systems. This paper presents a comprehensive survey of not only the state-of-the-art advances in metasurface-aided WPT and WEH systems, but also their applications to emerging technologies for future wireless networks such as wireless powered communication network (WPCN), simultaneous wireless information and power transfer (SWIPT), and millimeter wave (mmWave) communication. Besides discussing the research challenges and opportunities, we also present our proposed approach of harnessing metasurface technology to enhance endto-end energy delivery in future wireless networks.