rises in northwestern Wyoming in the Absaroka Range, on the Continental Divide in southwestern Park County. The river starts where the North Fork and the South Fork of the Yellowstone River converge. The North Fork, the larger of the two forks, flows from Younts Peak. The South Fork flows from the southern slopes of Thorofare Mountain. The Yellowstone River flows northward through Yellowstone National Park, feeding and draining Yellowstone Lake, then dropping over the Upper and Lower Yellowstone Falls at the head of the Grand Canyon of the Yellowstone within the confines of the park. After passing through the Black Canyon of the Yellowstone downstream of the Grand Canyon, the river flows northward into Montana between the northern Absaroka Range and the Gallatin Range in Paradise Valley. The river emerges from the mountains near the town of Livingston, where it turns eastward and northeastward, flowing across the northern Great Plains past the city of Billings.
East of Billings, it is joined by the Bighorn River. Further downriver, it is joined by the Tongue near Miles City, and then by the Powder in eastern Montana. It flows into the Missouri River near Buford, North Dakota just upstream from Lake Sakakawea.
In Montana the river has been used extensively for irrigation since the 1860s. In its upper reaches, within Yellowstone Park and the mountains of Montana, it is a popular destination for fly fishing. The Yellowstone is a Class I river from the Yellowstone National Park boundary to the North Dakota border for the purposes of stream access for recreational purposes. 
The division of water rights to the entire Yellowstone River Basin among Wyoming, Montana and North Dakota, governed by a 1950 compact, was disputed in a 2010 lawsuit brought directly in the U.S. Supreme Court by Montana against Wyoming. Oral argument took place in January 2011. On May 2, 2011, the Court held 7-2 (by Justice Thomas, with Justice Scalia dissenting) that Montana had no valid claim for diminution of its water, since Wyoming was irrigating the same acreage as always, albeit by a more modern method that returned less runoff to go downstream to Montana.  (A subsequent 2011 Supreme Court case, in which Montana asserted ownership of Missouri Basin riverbottoms, so as to collect decades of back rent from a hydropower company, is unrelated. On February 22, 2012, Montana lost that case too.)
The name is widely believed to have been derived from the Minnetaree Indian name Mi tse a-da-zi (Yellow Rock River) ( Hidatsa: miʔciiʔriaashiish').  Common lore states that the name came from the yellow-colored rocks along the Grand Canyon of the Yellowstone, but the Minnetaree never lived along the upper stretches of the Yellowstone. Some scholars think that the river was named after yellow-colored sandstone bluffs on the lower Yellowstone, instead.  The Crow Indians, who lived along the upper Yellowstone in Southern Montana, called it E-chee-dick-karsh-ah-shay (Elk River). Translating the Minnetaree name, French trappers called the river Roche Jaune (Yellow Rock), a name used by mountain men until the mid-19th century. Independently, Lewis and Clark recorded the English translation of Yellow Stone for the river, after encountering the Minnetaree in 1805. With expanding settlement by people from the United States, the English name eventually became the most widely used.  The river was explored in 1806 by William Clark during the return voyage of the Lewis and Clark Expedition. Clark's Fork of the river was named for him.
The Yellowstone River had long been an important artery of transportation for Native Americans. In the 19th century, European-American settlers depended on it as well, entering the region by riverboat. The region around the Big Horn, Powder and Tongue rivers is the traditional summer hunting grounds for numerous Native American tribes: Lakota Sioux, Crow, Cheyenne and Cree. Gold was discovered near Virginia City, Montana in the 1860s, and two of the primary routes for accessing the gold fields were the Bozeman Trail and the Bridger Trail both o