The purpose of this paper is to analyze the main issues concerned with the oxidative and storage stabilities of biodiesel and how they affect different metallic and polymeric materials present in automotive parts and in biodiesel storage structures. In addition, this work presents a review of the techniques used for measuring the oxidative stability and for evaluating the degradation of metallic and polymeric materials. When biodiesel is oxidized, a series of changes in its properties occurs. These changes not only affect biodiesel quality, but also the properties of the materials that are in contact with it. Upon oxidation, biodiesel properties like the acid value, peroxide value and viscosity increase, while the iodine value and the content of methyl esters decrease. The changes in the chemical and physical properties of biodiesel can affect the integrity and stability of the material. The situation reviewed in this paper, which talks about the stability of materials, could limit the extensive use of biodiesel. Such measures have been proposed in several countries, and it is a topic of great importance for biodiesel technology.