The Tarasov Mob is a russian with ran by the Tarasov family. Viggo was in charge of this organization. While in a bar Viggo sees John killing 3 people in a bar with a pencil. This led to Viggo asking John Wick to work with him. One day, John decides to leave due to his wife's illness. Viggo gave John an 'impossible task' to neutralise the other gang (which is currently unknown) this led to their Mob to keep existing until this day.
When Viggo Tarasov dies the crime family goes to his brother, Abram Tarasov. Abram tries to hide John's car and his gold. The Tarasov Mob's Crime family is decreasing in gang members due to John but are still in function. The new leader is Abram Tarasov.
The Tarasov Mob ran by a russian family called Tarasov. When Viggo's father died, Viggo was given the lead role in the organization which led to him running illegal businesses in a church and murder etc. The Tarasov Mob always had a rival gang (which is unknown). John neutralised this gang leading the gang's future to exist as said by Viggo Tarasov in John Wick (film).