The Lakota have 7 bands which are:

Oglala, or "they scatter their own."

Sicangu, or "burnt thighs."

Hunkpapa, or "end of the circle."

Miniconjous, or "planters beside the stream."

Sihasapa, or "Blackfeet."

Itazipacola, or "without bows."

Oohenupa, or "Two kettle."

There are also Dakota Sioux with 4 bands:  the Mdewakantonwon, the Wahpeton, the Wahpekute, and the Sisseton.

There were some chief's (like Red Cloud) who had some authority over their own bands, but the original social organization of the Lakota did not have a over all chief.  Each band had prominent warriors who were "shirt wearers."  When the bands gathered and camped together, 4 of these shirt wearers were selected by the tribal council of chiefs to be "wakicunsa" or camp leaders.  These leading shirt wearers had the overall authority over the entire camp circle.

In 1775, an Oglala war party traveling west from the Missouri River area came to the Black Hills.  The Black Hills were occupied at that time by the Cheyenne, along with the Kiowa and Crow.  But by 1794, the Oglala controlled the Black Hills, allowing the Cheyenne to remain in the area as allies.  The rest of the Lakota followed the lead of the Oglala into this general area.  

The Indians in this area traded almost exclusively with the French until about 1817 when the American traders began to compete for the buffalo fur business.  In 1825, the US sewed up the trade business with the 1825 Treaty between the US and the Oglala branch of the Sioux.  In the 1840's, an increasing flow of emigrants to Oregon and California brought cholera, smallpox, and measles to the Indians as well as accelerated buffalo hunting for the fur trade.  This caused hostility and some attacks against the emigrants and traders.  

In August, 1872, two railroad survey teams (each accompanied by about 500 troops) went into eastern Montana, and were attacked by bands led by Sitting Bull and Crazy Horse.  In March, 1873, General William Sherman testified before Congress, "This railroad is a national enterprise, and we are forced to protect the men during its survey and construction, through, probably the most warlike nation of Indians on this continent, who will fight for every foot of the line."  Of course the Indians did not believe that such activity was legal.  The chiefs who had signed the 1868 Treaty had not agreed to any railroads through their lands.

The areas south of the Platte in Nebraska, and up in eastern Montana became battlegrounds of competing interests.  In 1873, there was a major skirmish between the Oglala, Cheyenne's, and Hunkpapa and a railroad survey team led by General Custer, with a large military escort into the Black Hills themselves.  Rumors of gold in the Black Hills were already circulating, and a few hundred miners were illegally searching for gold in the Hills, and being attacked by Indians.

In 1874, some of the non-agency Lakota started operating in small war parties, attacking whites, settlers, and emigrants.  At first the US tried to stop the prospectors from moving into the Black Hills.  General Sheridan sent instructions to Brigadier General Alfred H. Terry to prevent companies of prospectors from trespassing on the Sioux reservation.  In the Spring of 1875, Red Cloud, Spotted Tail, and other chiefs were summoned to Washington to meet with President Grant and discuss the Black Hills.  The US wanted the Black Hills, and would send a commission later in the year to arrange a purchase price.  The Sioux didn't want this, and argued among themselves on what they should do.  The US Senate Commission visited the Nebraska agencies in 1875, and tried to negotiate an outright purchase price for the Black Hills.  They wanted to buy them for $6 million.  The chief's had other ideas.  Some were willing to sell for $600 million and food supplies for another seven generations of Sioux.  Others refused to sell at any cost.  

President Grant then decided to abandon the US Treaty obligation to preserve the Lakota territory.  With the Army no longer enforcing the Treaty, the invasion of settlers and miners into the Black Hills increased.  It was a wild and violent situation, with Indians attacking miners, miners and settlers attacking Indians, and outlaws against Indians and miners alike.  The US government decided that the only remaining option was to protect the US citizens mining in the Black Hills for gold.  On December 6, 1875, the US Commissioner on Indian Affairs ordered the Lakota onto the reservation by a January 31, 1876 deadline.  They were threatened as "hostiles" if they didn't meet the deadline.  The Sioux bands were scattered during this harsh winter; some didn't get the order; others were hunting or camped in the Unceded Indian Territory (which was their right).  It would also have been impossible to move thousands of women and children through the snows to the reservation in this short time, and no food for them if they got there.  On February 1, 1876, the Secretary of the Interior relinquished jurisdiction over all so called "hostile" Sioux to the War Department.  The Army was ordered in, and the 1868 Treaty was demolished.  

In September 1876, when the US military occupied the Black Hills and forced the Sioux to surrender, the US demanded the Lakota sign over the Black Hills and accept subsistence rations on the reservations or starve.  Some Lakota leaders (including Red Cloud and Spotted Tail) were coerced to sign the 1876 Treaty to avoid mass starvation of their people.  They did so under vocal protest to save their people.  Only 10% of the adult male Sioux agreed (of the 75% required by the 1868 Treaty).  Therefore, this treaty was invalid.  Congress enacted this faulty agreement into law in February, 1877.  This was in effect a unilateral abrogation of the 1868 Treaty by the US.  The issue continued to be disputed for more than another hundred years, through the Supreme Court decision of 1980 to award interest on payments to the Sioux for the US taking the Black Hills in violation of the 1868 Treaty.

For the US, the issue has come down to one of compensation.  About $500 million in payment and interest since 1877 are in an account the Lakota refuse to touch.  The Lakota have never surrendered their moral claim to their Black Hills homeland.