Oligarchies are when a small group of usually wealthy people, or families, control a government, frequently over a number of generations.
These individuals don’t always have official government positions, but usually due to their wealth and connections, they have an easy time being elected to positions.
Oligarchies are probably the most common form of government around the world. Even within the most democratic parliamentary systems, like Britain, The United States, Canada and all over Europe, small numbers of wealthy people are able to manipulate the political levers through campaign contributions and sponsorhip of candidates.
Oligarchies are alive and well.