Owing to the growing concerns about the dwindling fossil fuel reserves, increasing energy demand, and climate emergency, it is imperative to develop and deploy sustainable energy technologies to ensure future energy supply and to transition to the net-zero world. In this context, there is great potential in the biorefinery concept for supplying drop in biofuels in the form of biodiesel. Biodiesel as a fuel can certainly bridge the gap where electrification or the use of hydrogen is not feasible, for instance, in heavy vehicles and in the farm and marine transportation sectors. However, the biodiesel industry also generates a large amount of crude glycerol as the by-product. Due to the presence of several impurities, crude glycerol may not be a suitable feedstock for all high-value products derived from glycerol, but it fits well with glycerol esterification for producing glycerol acetins, which have numerous applications. This review critically looks at the processes using nanostructured solid/liquid acid catalysts for glycerol esterification, including the economic viability of the scale-up. The homogeneous catalysts reviewed herein include mineral acids and Brønsted acidic ionic liquids, such as SO3H-functionalized and heteropoly acid based ionic liquids. The heterogeneous catalysts reviewed herein include solid acid catalysts such as metal oxides, ion-exchange resins, zeolites, and supported heteropoly acid-based catalysts. Furthermore, the techno-economic analysis studies have shown the process to be highly profitable, confirming the viability of glycerol esterification as a potential tool for economic value addition to the biorefinery industry.