Exploration of yeast diversity for the sustainable production of biofuels, in particular biodiesel, is gaining momentum in recent years. However, sustainable, and economically viable bioprocesses require yeast strains exhibiting: (i) high tolerance to multiple bioprocess-related stresses, including the various chemical inhibitors present in hydrolysates from lignocellulosic biomass and residues; (ii) the ability to efficiently consume all the major carbon sources present; (iii) the capacity to produce lipids with adequate composition in high yields. More than 160 non-conventional (non-Saccharomyces) yeast species are described as oleaginous, but only a smaller group are relatively well characterised, including Lipomyces starkeyi, Yarrowia lipolytica, Rhodotorula toruloides, Rhodotorula glutinis, Cutaneotrichosporon oleaginosus and Cutaneotrichosporon cutaneum. This article provides an overview of lipid production by oleaginous yeasts focusing on yeast diversity, metabolism, and other microbiological issues related to the toxicity and tolerance to multiple challenging stresses limiting bioprocess performance. This is essential knowledge to better understand and guide the rational improvement of yeast performance either by genetic manipulation or by exploring yeast physiology and optimal process conditions. Examples gathered from the literature showing the potential of different oleaginous yeasts/process conditions to produce oils for biodiesel from agro-forestry and industrial organic residues are provided.