The Dutch naturalist Antonie van Leeuwenhoek is often credited as the inventor of the microscope, and in 1680 he became the first person to observe yeast under one. Wikipedia reports, somewhat confusingly, that "at the time [he] did not consider them to be living organisms, but rather globular structures as researchers were doubtful whether yeasts were algae or fungi."
Well ... whether they're algae or fungi, they're still living organisms.
Anyway ... it was the German physician and physiologist Theodor Schwann who, in 1837, recognised that yeast was a fungus.
Louis Pasteur, a French microbiologist, proved in 1857 that alcoholic fermentation was conducted by living yeasts and not by a chemical catalyst. Pasteur also found that the fermentation process is inhibited by the presence of oxygen, so alcohol production is commonly carried out under a blanket of carbon dioxide to reduce the amount of oxygen present.
Australia's (self–styled) "#1 Online Craft Beer Store" has an interesting page about the history of yeast and its role in brewing beer.
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