Kodak began as a partnership between George Eastman and Henry A. Strong to develop a film roll camera. After the release of the Kodak camera, Eastman Kodak was incorporated on May 23, 1892. Under Eastman's direction, the company became one of the world's largest film and camera manufacturers, and also developed a model of welfare capitalism and a close relationship with the city of Rochester. During most of the 20th century, Kodak held a dominant position in photographic film, and produced a number of technological innovations through heavy investment in research and development at Kodak Research Laboratories. Kodak produced some of the most popular camera models of the 20th century, including the Brownie and Instamatic. The company's ubiquity was such that its "Kodak moment" tagline entered the common lexicon to describe a personal event that deserved to be recorded for posterity.

Kodak began to struggle financially in the late 1990s as a result of increasing competition from Fujifilm. The company also struggled with the transition from film to digital photography, although Kodak had developed the first self-contained digital camera. Attempts to diversify its chemical operations failed, and as a turnaround strategy in the 2000s, Kodak instead made an aggressive turn to digital photography and digital printing. These strategies failed to improve the company's finances, and in January 2012, Kodak filed for Chapter 11 bankruptcy protection in the United States Bankruptcy Court for the Southern District of New York.^[

In September 2013, the company emerged from bankruptcy, having shed its large legacy liabilities, restructured, and exited several businesses. Since emerging from bankruptcy, Kodak has continued to provide commercial digital printing products and services, motion picture film, and still film, the last of which is distributed through the spinoff company Kodak Alaris. The company has licensed the Kodak brand to several products produced by other companies, such as the PIXPRO line of digital cameras manufactured by JK Imaging. In response to the COVID-19 pandemic in 2020, Kodak announced in late July that year it would begin production of pharmaceutical materials.

The letter k was a favorite of George Eastman's; he is quoted as saying, "it seems a strong, incisive sort of letter." He and his mother, Maria, devised the name Kodak using an Anagrams set. Eastman said that there were three principal concepts he used in creating the name: it should be short, easy to pronounce, and not resemble any other name or be associated with anything else. According to a 1920 ad, the name "was simply invented – made up from letters of the alphabet to meet our trade-mark requirements. It was short and euphonious and likely to stick in the public mind." The Kodak name was trademarked by Eastman in 1888. There was also a rumour that the name Kodak came from the sound made by the Kodak camera's shutter.

In 1888, the Kodak camera was patented by Eastman. It was a box camera with a fixed-focus lens on the front and no viewfinder; two V shape silhouettes at the top aided in aiming in the direction of the subject. At the top it had a rotating key to advance the film, a pull-string to set the shutter, and a button on the side to release it, exposing the celluloid film. Inside, it had a rotating bar to operate the shutter. When the user pressed the button to take a photograph, an inner rope was tightened and the exposure began. Once the photograph had been taken, the user had to rotate the upper key to change the selected frame within the celluloid tape.

The $25 camera came pre-loaded with a film roll of 100 exposures, and could be mailed to Eastman's headquarters in Rochester with $10 for processing. The camera would be returned with prints, negatives, and a new roll of film. Additional rolls were also sold for $2 to professional photographers who wished to develop their own photographs. By unburdening the photographer from the complicated and expensive process of film development, photography became more accessible than ever before. The camera was an immediate success with the public and launched a fad of amateur photography. Eastman's advertising slogan, "You Press the Button, We Do the Rest", soon entered the public lexicon, and was referenced by Chauncey Depew in a speech and Gilbert and Sullivan in their opera Utopia, Limited.

In the 1890s and early 1900s, Kodak grew rapidly and outmaneuvered competitors through a combination of innovation, acquisitions, and exclusive contracts. Eastman recognized that film would return more profit than the cameras that used them, and focused on control of the film market. This razor and blades model of sales would change little for several decades. Larger facilities were soon needed in Rochester, and the construction of Kodak Park began in 1890. Kodak purchased and opened several shops and factories in Europe, particularly in the United Kingdom. The British holdings were initially organized under the Eastman Photographic Materials Company. Beginning in 1898, they were placed under the holding company Kodak Limited. An Australian subsidiary, Australia Kodak Limited, was established in 1908. In 1931, Kodak-Pathé was established in France and Kodak AG was formed in Germany following the acquisition of Nagel. The Brownie camera, marketed to children, was first released in 1900, and further expanded the amateur photography market. One of the largest markets for film became the emerging motion picture industry. When Thomas Edison and other film producers formed the Motion Picture Patents Company in 1908, Eastman negotiated for Kodak to be sole supplier of film to the industry. In 1914, Kodak built its current headquarters on State Street. By 1922, the company was the second-largest purchaser of silver in the United States, behind the U.S. Treasury. Beginning on July 18, 1930, Kodak was included in the Dow Jones Industrial Average.

During World War I, Kodak established a photographic school in Rochester to train pilots for aerial reconnaissance. The war strained supply chains, and Eastman sought out new chemical sources the company could have direct control over. At the war's end in 1920, Kodak purchased a hardwood distillation plant in Tennessee from the federal government and established Eastman Tennessee, which later became the Eastman Chemical Company.

Henry Strong died in 1919, after which Eastman became the company president. Eastman began to wind down his involvement in the daily management of the company in the mid-1920s, and formally retired in 1925, although he remained on the board of directors. William Stuber succeeded him as president, and managed the company along with Frank Lovejoy.