Biodiesel has gained much attention as it is a promising renewable substitute fuel to conventional diesel in the future. Although biodiesel has numerous advantages such as lower toxicity, higher flash point and its biodegradability over conventional diesel, the challenges of its poor cold flow properties and oxidation stability limit its application. This is attributed to the high level of polyunsaturated fatty acid methyl esters in the biodiesel feedstock. Oxidation stability is determined by the fatty acid compositions and natural antioxidants of the biodiesel. A higher amount of unsaturated fatty acid methyl esters are susceptible to oxidative degradation and this in turns shortens the induction period and improves the cold flow properties of the biodiesel. Conversely, a full saturated fatty acid also results in higher cetane number and increases the oxidation stability of the biodiesel but tends to worsen the cold flow properties and this may result in low heating value and high viscosity which may affect the engine in a negative way during lower temperature climate especially winter. Partial hydrogenation of biodiesel is one of the techniques to improve the challenges of cold flow properties and oxidation stability. This review paper seeks to summarize the developments in terms of the production, cold flow properties, oxidation stability, catalytic material for the hydrogenation process, and feedstock for the production and ways to reduce trans-isomers in hydrogenated biodiesel.