Biodiesel is a promising renewable energy carrier, providing a sustainable alternative to conventional petroleum diesel. Produced primarily through the transesterification of oils and fats into fatty acid methyl esters (FAME), biodiesel offers several environmental and performance advantages, including reduced greenhouse gas emissions, carbon neutrality, biodegradability, and a higher cetane number. Despite its technical feasibility and established commercial applications, large-scale adoption is constrained by production costs, feedstock limitations, and fuel property challenges such as cold flow behaviour. This review consolidates current knowledge on biodiesel production with a particular focus on the role of feedstocks, technological methodologies, and process equipment. This review work compares edible and non-edible vegetable oils, animal fats, waste oils, and microalgae with respect to their advantages, limitations, and sustainability profiles. Production techniques—including base-catalysed transesterification, acid esterification, supercritical alcohol processes, and thermochemical routes—have been critically examined alongside reactor designs, separation units, and purification systems. The review also highlights quality testing standards such as ASTM D6751 and EN 14214, which govern biodiesel commercialization. The findings of this research work suggest that future development of biodiesel depends on diversifying sustainable feedstocks, advancing catalysts and reactor technologies, and integrating cost-effective waste valorization strategies. This work finally concludes with the observation that biodiesel can become a cornerstone in achieving low-carbon transport systems supporting the global transition to renewable energy.