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Biodiesel is a renewable fuel that is suitable for both stationary and automotive engines. It consists of fatty acid methyl esters and fatty acid ethyl esters when vegetable oils are transesterified with methanol and ethanol respectively. The structural configuration and properties of individual fatty acid methyl esters can significantly influence the biodiesel properties. The purpose of the present work is to review the effects of the properties and the structural configurations of fatty acid methyl esters on various biodiesel properties. The structural configuration includes the molecular structure, the chain length, the saturated or unsaturated nature, the degree of unsaturation and the position of double bonds. Important properties of fatty acid methyl esters are reviewed, and a large number of data consisting of their reported values are given. The viscosity, the cetane number, the heat of combustion, the density, the bulk modulus and compressibility, the iodine value, the oxidative stability, the low-temperature properties, the boiling point, the lubricity, the saponification value, the surface tension, the specific heat, the latent heat of vaporization and the flash point are reviewed in the present study. The reported mathematical equations for estimating the properties of fatty acid compounds and biodiesel are presented. A few studies that recommend enrichment of a particular fatty acid (or acids) which is possible through genetic modification to improve the overall biodiesel properties are also cited. The contribution of a particular fatty acid (or acids) favours some properties while it has an undesirable effect on other properties. Hence the specification of one particular fatty acid profile to improve all the properties of biodiesel is not possible. Considering the low-temperature properties and the oxidative stability, a combination of both saturated fatty acids and unsaturated fatty acids is necessary. Therefore, it is important to decide whether a biodiesel should contain a larger amount of saturated fatty acid esters or unsaturated fatty acid esters in order to obtain better fuel properties. The inherent genetic modification of the fatty acid profile could be the best possibility for addressing several fuel property issues simultaneously.