Triglycerides are the main constituents of lipids, which are the fatty acids of glycerol. Natural organic triglycerides (viz. virgin vegetable oils, recycled cooking oils, and animal fats) are the main sources for biodiesel production. Biodiesel (mono alkyl esters) is the most attractive alternative fuel to diesel, with numerous environmental advantages over petroleum-based fuel. The most practicable method for converting triglycerides to biodiesel with viscosities comparable to diesel fuel is transesterification. Previous research has proven that biodiesel–diesel blends can operate the compression ignition engine without the need for significant modifications. However, the commercialization of biodiesel is still limited due to the high cost of production. In this sense, the transesterification route is a crucial factor in determining the total cost of biodiesel production. Homogenous base-catalyzed transesterification, industrially, is the conventional method to produce biodiesel. However, this method suffers from limitations both environmentally and economically. Although there are review articles on transesterification, most of them focus on a specific type of transesterification process and hence do not provide a comprehensive picture. This paper reviews the latest progress in research on all facets of transesterification technology from reports published by highly-rated scientific journals in the last two decades. The review focuses on the suggested modifications to the conventional method and the most promising innovative technologies. The potentiality of each technology to produce biodiesel from low-quality feedstock is also discussed.