Back in the third and fourth centuries there were fermented rice drinks, but they were crude and not really the same type of beverage that we think of today as saké. By the fifth or sixth century the favorite alcoholic beverage in Japan was a drink similar to modern saké, made from rice, water, and kōji mold. This combination of rice, water and fermenting agent (yeast and kōji) is the basis for making all Nihonshu (日本酒), or Japanese saké. When drinks similar to saké became popular is hard to say, but rice-based alcohol had been referred to centuries earlier.
In 689 the imperial palace in Nara established a saké brewing department. That was the first time goverment took an active interest in saké and Nara really became the brewing center for standardized saké. In the eighth and ninth centuries saké began to resemble modern saké as new innovations began to change saké manufacturing.
By the tenth, eleventh and twelfth centuries, saké production was mastered in the temples throughout Japan. They introduced most of the modern brewing innovations that we employ today. These include the three step brewing process used to this day by saké manufacturers, adding ingredients to the mash in each step.
Another of these innovations that followed in the next few centuries as the temples further refined their craft was pasteurization. Yes, for those of you paying attention, this was long before the birth of Louis Pasteur. Later in the sixteenth century Kyoto was the new capital, and became the center of the saké world, and saké brewers began to significantly improve the quality of their sakés.
The next important stage in saké evolution happened in the late nineteenth century, as legal reforms allowed anyone to setup saké production. An explosion of saké production was the result, as more than 30,000 saké manufacturers sprang up. The government came to regard this boom as an opportunity to collect revenue, and began to whittle down the ranks of the saké manufacturers.
In the 20th century major innovations were incorporated into the brewing of saké. Cross breeding strains of rice continues to this day; important because different types of rice produce different tasting sakés. Computerization has played an increasingly important role in the brewing process to control conditions more precisely and monitor the process more effectively. Technology continues to improve the rice milling operations as well; it is very difficult to remove large amounts of the rice's outer layers and employing better milling machinery has come to make a huge difference.
After the rice rationing of World War II led to drastic diminishment of the quality of saké produced, saké began a comeback. Saké began to enjoy unprecedented popularity in Japan, peaking in the 1970's. Today saké consumption in Japan continues to decline, even as it's popularity in the United States and elsewhere is trending upward strongly. Much like what happened to the wine industry, quality saké production has spread across continents and now is maturing in places like China, USA, Australia and other countries.