South Dakota consists of four major land regions: the Drift Prairie, the Dissected Till Plains, the Great Plains, and the Black Hills.

The Drift Prairie covers most of eastern South Dakota. This is the land of low hills and glacial lakes. This area was called Coteau des Prairies (Prairie Hills) by early French traders. In the north, the Coteau des Prairies is bordered on the east by the Minnesota River Valley and on the west by the James River Basin. The James River Basin is mostly flat land, following the flow of the James River through South Dakota from north to south.

The Dissected Till Plains lie in the southeastern corner of South Dakota. This area of rolling hills is criss-crossed by many streams.

The Great Plains cover most of the western two-thirds of South Dakota. The Coteau de Missouri hills and valleys lie between the James River Basin of the Drift Prairie and the Missouri River. West of the Missouri River the landscape becomes more rugged and consists of rolling hills, plains, canyons, and steep flat-topped hills called buttes. These buttes sometimes rise 400 to 600 feet (120 to 180 m) above the plains. In the south, east of the Black Hills, lie the South Dakota Badlands.

The Black Hills are in the southwestern part of South Dakota and extend into Wyoming. This range of low mountains covers 6,000 square miles (15,500 km².) with mountains that rise from 2,000 to 4,000 feet (600 to 1,200 m) above their bases. The highest point in South Dakota, Harney Peak (7,242 ft or 2,207 m above sea level), is in the Black Hills. The Black Hills are rich in minerals such as gold, silver, copper, and lead. The Homestake Mine, one of the largest gold mines in the United States, is located in the Black Hills.

President Thomas Jefferson organized a group called the Corps of Discovery, led by Meriwether Lewis and William Clark (commonly referred to as "Lewis and Clark Expedition"), to explore the newly-acquired region. In 1817, an American fur trading post was set up at present-day Fort Pierre, beginning continuous American settlement of the area. Through much of the 19th century, exploratory expeditions such as those of Lewis and Clark and Joseph Nicollet coincided with an increasing presence of the U.S. Army. In 1855, the U.S. Army bought Fort Pierre but abandoned it the following year in favor of Fort Randall to the south. Settlement by Americans and Europeans was, by this time, increasing rapidly, and in 1858, the Yankton, Dakota, and Sioux resigned themselves to signing the 1858 Treaty, ceding most of present-day eastern South Dakota to the United States. Of this, Yankton leader Strike-the-Ree said "The white men are coming like maggots. It is useless to resist them.... Many of our brave warriors would be killed, our women and children left in sorrow, and still we would not stop them."

Land speculators founded two of eastern South Dakota's largest present-day cities: Sioux Falls in 1856 and Yankton in 1859. In 1861, Dakota Territory was recognized by the United States government (this initially included North Dakota, South Dakota, and parts of Montana and Wyoming). Settlers from Scandinavia, Germany, Ireland, and Russia, as well as elsewhere in Europe and from the eastern U.S. states, increased from a trickle to a flood, especially after the completion of an eastern railway link to the territorial capital of Yankton in 1872, and the discovery of gold in the Black Hills in 1874 during a military expedition led by George A. Custer. This expedition took place despite the fact that all of Dakota Territory west of the Missouri River (along with much of Nebraska, Montana, and Wyoming) had been granted to the Sioux by the Treaty of 1868 as part of the Great Sioux Nation. The Sioux declined to grant mining rights or land in the Black Hills, and war broke out after the U.S. failed to stop white miners and settlers from entering the region.

Native Americans were unable to compete with the greater numbers and superior weaponry available to U.S. forces. They were also hampered by the sharp decline in numbers of the buffalo, which was a major food source of the Sioux. Between 1878 and 1886, the Euro-American settler population of eastern Dakota Territory tripled. The last major incident in this struggle occurred on December 29, 1890, at Wounded Knee Creek in present-day western South Dakota, when U.S. soldiers massacred as many as 300 Sioux, mostly women and children. Just over a year earlier, on November 2, 1889, Dakota Territory was incorporated into the United States as the modern states of North Dakota and South Dakota.

Currently, there are 35 members of the state Senate and 70 members of the House of Representatives. The state is comprised of 35 legislative districts. Voters elect 1 senator and 2 representatives from each district. The legislature meets once a year on the second Tuesday in January, and also if the governor calls a special session.

The state Supreme Court is the highest court in South Dakota and the court of last resort for state appellate actions. The chief justice and four justices comprise the South Dakota Supreme Court. South Dakota is divided into seven judicial circuits. There are 38 circuit judges serving in the seven circuits. Circuit courts are the state's trial courts of general jurisdiction. There are 12 full-time and 3 part-time magistrate judges in the seven circuits. Magistrate courts assist the circuit courts in disposing of misdemeanor criminal cases and minor civil actions. These courts of limited jurisdiction make the judicial system more accessible to the public by providing a means of direct court contact for the average citizen.

South Dakota does not levy inheritance taxes, personal or corporate income taxes or taxes on intangible personal property. The state sales tax is 4 percent.

Personal and property taxes are local taxes and are the primary source of funding for school systems, counties, municipalities and other local government units. Their administration is a local responsibility. The state revenue department does not collect or use property taxes, but it does centrally assess the property of large companies. Property owners in South Dakota may be taxed by two or more of the following units of government: cities, counties, townships, school districts, water districts, and, in some cases, units such as fire and sanitary sewer districts.