An example of Social Darwinism that most people will know about is the concentration camps set up by the Nazis during WWII. This is a very well known example of the eugenics movement. The Nazis wished to eliminate certain groups such as the Jews, homosexuals, persons with mental illness or disabilities, and others.
Poor, mentally ill, disabled, immigrant, "immoral," and many other groups of people were sexually sterilized, sometimes without their knowledge or consent. These sterilizations were a type of eugenics in order to prevent "undesirable traits" from being passed on. This happen in America, with a large number of states in America adopting laws to allow forced sterilization during the early parts of the 20th century.
You can learn more about forced sterilizations in this documentary on eugenics: The Eugenics Crusade
The Black War, as it would be later called, was a terrible conflict between the British Empire and the Aboriginal Tasmanian people in the 1820s. British colonizers moved to Tasmania where 5,000 Tasmanian people had been living out of the reach of the outside world for thousands of years. These colonizers saw the Tasmanians as savages who did not deserve to live, and, although it was against the law, they began attacking the Tasmanians. Murder, disease, and kidnapping were common during those times, and many of the Tasmanian people did not survive. When there were very few Tasmanian people left, the governor of the British citizens hired a man who had been converting the Tasmanian people to Christians to relocate the remaining people to a new island where they could be taught to be civilized Christians. 300 Tasmanians were taken to this new island and given land, a chapel, and houses. They did this in order to make these "savages" into successful Christian people. 240 of them died by the 1840s in these conditions.
Learn more about this in the documentary: A History on the Fatal Impact Racial Imperialism
There was a movement in America to assimilate Native Americans to the lifestyle that would help "Americanize" them. Religious reformers would come in and try to convert these people to their religion and lifestyles. Sometimes their culture and religion was considered below those of the reformers. Their land, culture, and practices were taken from them. Sometimes children would be taken and put into religious boarding schools. Some other groups of people thought that Native Americans were below them. This caused serious conflict between the groups.
Humans from different ethnic and racial groups were put into zoos and exhibits in the name of "learning." Early examples of ethnological exhibits were mostly found in freak show attractions. It was not until later on that these exhibits started being used for "scientific" purposes. Indigenous people from around the world were shown off as a missing link between civilized man and monkeys. These were extremely racist exhibits, and sometimes the person would be put on display in a cage next to a monkey. The St. Louis World Fair in 1904 had the largest Human Zoo in history, having many different types of indigenous people on display for Americans to view.
History tends to repeat itself, and there is potential for further problems with eugenics. Genetic engineering is something that has become increasingly common in recent years. There has been interest in potentially genetically engineering human embryos. While it is considered unethical by most of the world, scientists in China have actually already modified the genetic code of human embryos, two of which were born in 2018. While the technology for this is extremely limited at the present time, there is future potential for terrible consequences if it is not managed properly. Some fictional examples of potential problems with this include: Gattaca and Brave New World.