Short answers, pulled from the story.
Oligarchy is a form of government in which power rests with a small number of people, typically characterized by wealth or nobility. Political scientist Jeffrey Winters notes that democracy and oligarchy can coexist, but tension arises when a majority of voters opposes the unequal wealth distribution that oligarchs tend to protect.
Winters and Page identify four main mechanisms: lobbying to shape tax and other policies, campaign contributions to influence who wins elections, opinion shaping to control who is heard by decision-makers, and manipulation of constitutional rules including judicial appointments. Oligarchs do not need to hold formal government positions because indirect influence is sufficient.
The Thirty Tyrants were an oligarchy installed by Sparta after Athens surrendered in the Peloponnesian War. They ruled from 404 BC to 403 BC, a period of only eight months, but killed five percent of the Athenian population, confiscated citizens' property, and exiled democratic supporters.
After the Soviet Union dissolved in 1991, rapid privatization of state assets allowed a new class of business oligarchs to take control of significant portions of the Russian economy, especially in energy, metals, and natural resources. In 1996, a group known as the Seven Bankers funded Boris Yeltsin's re-election campaign; after Vladimir Putin came to power in 1999, he cracked down on many of them but eventually created a new oligarch class from his own personal circle.
Martin Gilens of Princeton and Benjamin Page of Northwestern analyzed American policy outcomes between 1981 and 2002 and concluded that wealthy individuals and business groups held substantial influence over political decisions, often sidelining average citizens. Gilens and Page did not label the United States an outright oligarchy but found strong evidence of economic elites dominating certain areas of policymaking.
In 2015, former president Jimmy Carter described the United States as an "oligarchy with unlimited political bribery," citing the 2010 Citizens United v. FEC Supreme Court decision, which removed limits on donations to political campaigns.
George Bernard Shaw coined the concept of intellectual oligarchy in his 1907 play Major Barbara. Shaw criticized the control of society by professional elites including lawyers, doctors, priests, and politicians, and called for a democratic power strong enough to compel the intellectual oligarchy to serve the general good.