Before joining Vigilance, Jason Greenfield used the DarkNet under the alias Atlas7. Finch found chat logs praising Atlas7 for his hacking of government websites to release top-secret information to the public. (“Mors Praematura”)
Owen Matthews's activities on the DarkNet turned him into a target for several drug cartels and the ISA. (“4C”)
Black Market Bazaar - the biggest narcotics trafficking website which was created by Owen Matthews. The website was shut down by the FBI, but while active was considered the "eBay of narcotics". (“4C”)
The DarkNet on Person of Interest reminds of the actual Deep Web, an underlying part of the Internet that is not indexed by regular search engines, and only accessible through dedicated software such as TOR. There is a real-world network called Darknet which is mainly associated with file sharing and underground web communication.
In “Mors Praematura”, Vigilance uses a secure TOR network to communicate with other Vigilance members nationwide which maintains the anonymity of the user's internet traffic from anyone conducting network surveillance or traffic analysis.
The Black Market Bazaar appears to be modeled after Silk Road, an anonymous marketplace for illegal items and pirated goods which was shutdown in 2013.