Unmanned Aerial Vehicles (UAVs) or drones have witnessed a spectacular surge in applications for military, commercial, and civilian purposes. However, their potential for flight is always limited by the finite power budget of their onboard power supplies. The limited flight time problem has led to intensive research into new sources of power and innovative charging strategies to enable protracted, autonomous flight. This paper gives a comparative summary of the current state-of-the-art in UAV power and refuelling technology. The paper begins with an analysis of the variety of energy sources, from classical batteries to fuel cells and hybrid systems, based on their relative advantages and disadvantages in energy density, weight, and safety. Subsequently, the review explores a spectrum of replenishment options, from simple manual battery swapping to sophisticated high-tech automatic docking stations and smart contact-based charging pads. Most of the review is dedicated to the newer technology of wireless power transfer, which involves near-field (inductive, capacitive) and far-field (laser, microwave) technology. The article also delves into the most important power electronic converter topologies, battery management systems, and control approaches that form the core of these charging systems. Finally, it recapitulates the most significant challenges in technical, economic, and social aspects for promising avenues of future research. The comprehensive review is a valuable guide for researchers, engineers, and policymakers striving to enhance UAV operational performance.