Metasurface Energy Harvesters (MEHs) have emerged as a prominent enabler of highly efficient Radio Frequency (RF) energy harvesters. This survey delves into the fundamentals of the MEH technology, providing a comprehensive overview of their working principle, unit cell designs and prototypes over various frequency bands, as well as state-of-the art modes of operation. Inspired by the recent academic and industrial interest on Reconfigurable Intelligent Surfaces (RISs)for the upcoming sixth-Generation (6G) of wireless networks, we study the interplay between this technology and MEHs aiming for energy sustainable RISs power by metasurface-based RF energy harvesting. We present a novel hybrid unit cell design capable of simultaneous energy harvesting and 1-bit tunable reflection whose dual-functional response is validated via full-wave simulations. Then, we conduct a comparative collection of real-world measurements for ambient RF power levels and power consumption budgets of reflective RISs to unveil the potential for a self-sustainable RIS via ambient RF energy harvesting. The paper is concluded with an elaborative discussion on open design challenges and future research directions for MEHs and energy sustainable hybrid RISs.