Presently, the use of fossil fuels is not ecologically sustainable, which results in the need for new alternative energies such as biodiesel. This work presents a review of the classification of the lipidic feedstocks and the catalysts for biodiesel production. It also presents the pros and cons of the different processes and feedstocks through which biodiesel is obtained. In this context, cooking oil (WCO) has emerged as an alternative with a high potential for making the process sustainable. A detected limitation to achieving this is the high content of free fatty acids (FFA) and existing problems related to homogeneous and heterogeneous catalysts. To overcome this, the use of bifunctional catalysts is being evaluated by the scientific community. Thus, this work also explores the advances in the study of bifunctional catalysts, which are capable of simultaneously carrying out the esterification of free fatty acids (FFA) and the triglycerides present in the WCO. For the sake of an improved understanding of biodiesel production, flow diagrams and the mechanisms implied by each type of process (enzymatic, homogenous, and heterogeneous) are provided. This article also highlights some of the challenges in catalyst development for sustainable biodiesel production from low-grade raw materials.