Lipid-based biofuels, such as biodiesel and hydroprocessed esters, are a central part of the global initiative to reduce the environmental impact of the transport sector. The vast majority of production is currently from first-generation feedstocks, such as rapeseed oil, and waste cooking oils. However, the increased exploitation of soybean oil and palm oil has led to vast deforestation, smog emissions and heavily impacted on biodiversity in tropical regions. One promising alternative, potentially capable of meeting future demand sustainably, are oleaginous yeasts. Despite being known about for 143 years, there has been an increasing effort in the last decade to develop a viable industrial system, with currently around 100 research papers published annually. In the academic literature, approximately 160 native yeasts have been reported to produce over 20% of their dry weight in a glyceride-rich oil. The most intensively studied oleaginous yeast have been Cutaneotrichosporon oleaginosus (20% of publications), Rhodotorula toruloides (19%) and Yarrowia lipolytica (19%). Oleaginous yeasts have been primarily grown on single saccharides (60%), hydrolysates (26%) or glycerol (19%), and mainly on the mL scale (66%). Process development and genetic modification (7%) have been applied to alter yeast performance and the lipids, towards the production of biofuels (77%), food/supplements (24%), oleochemicals (19%) or animal feed (3%). Despite over a century of research and the recent application of advanced genetic engineering techniques, the industrial production of an economically viable commodity oil substitute remains elusive. This is mainly due to the estimated high production cost, however, over the course of the twenty-first century where climate change will drastically change global food supply networks and direct governmental action will likely be levied at more destructive crops, yeast lipids offer a flexible platform for localised, sustainable lipid production. Based on data from the large majority of oleaginous yeast academic publications, this review is a guide through the history of oleaginous yeast research, an assessment of the best growth and lipid production achieved to date, the various strategies employed towards industrial production and importantly, a critical discussion about what needs to be built on this huge body of work to make producing a yeast-derived, more sustainable, glyceride oil a commercial reality.