In 1769, the last big Tatar raid into Southern Russian territories captured thousands of slaves. These were mostly sold into Ottoman territories.

Soon afterwards, in 1774, Russia invaded the Crimea and forced it to become a vassal state, later annexing it in 1783. The Russian military had finally defeated the Tartars and forced the end of major slaving raids into Russia.

The Barbary Pirates sacked towns and villages around the coasts of the Mediterranean and enslaved the inhabitants, as well as capturing ships and enslaving the crew and passengers, up until the early 1800s. It was the French conquest of Algiers, in 1830, which finally stopped this.

ISIS is selling the civilians of sacked and conquered cities into slavery today.

Unfortunately, the selling of the civilians of a sacked city into slavery has not stopped.

The usual 'why' it stopped in the past has been the application of overwhelming military force.