The last years there has been a significant rise in the number of publications in the international literature that deal with the production of lipids by microbial sources (the 'single cell oils; SCOs' that are produced by the so-called 'oleaginous' micro-organisms). In the first part of the present review article, a general overview of the oleaginous micro-organisms (mostly yeasts, algae and fungi) and their potential upon the production of SCOs is presented. Thereafter, physiological and kinetic events related with the production of, mostly, yeast and fungal lipids when sugars and related substrates like polysaccharides, glycerol, etc. (the de novo lipid accumulation process) or hydrophobic substrates like oils and fats (the ex novo lipid accumulation process) were employed as microbial carbon sources, are presented and critically discussed. Considerations related with the degradation of storage lipid that had been previously accumulated inside the cells, are also presented. The interplay of the synthesis of yeast and fungal lipids with other intracellular (i.e. endopolysaccharides) or extracellular (i.e. citric acid) secondary metabolites synthesized is also presented. Finally, aspects related with the lipid extraction and lipidome analysis of the oleaginous micro-organisms are presented and critically discussed.