Vigilantes are individuals hired by the Novus Orbis Librarium to capture criminals and bring them to the organization for a monetary reward. There are rules and legislation that keep vigilantes in check.
The vigilante system was established sometime after the Dark War as part of the NOL's response to hostile wildlife and mutated creatures birthed from the Black Beast's seithr. With the establishment of the Hierarchical Cities, there was no longer a need to suppress the wildlife. However, during this time crime spiralled out of control. The NOL was reluctant to deploy soldiers to catch common criminals, as their soldiers were considered elite and often moved in units, so the NOL repurposed the vigilante as a kind of police force.
There are no forms to sign or exams to take to become a vigilante, and as such, being a vigilante is not an official position.  Because of this, anyone can become a vigilante — some vigilantes even hold normal jobs on the side. However, there is a set of rules that all vigilantes must adhere to, known as the Four Vigilantes' Agreements. Vigilantes are also obligated to provide information to the NOL.
Vigilantes are given a binding Ars Magus to restrain criminals. Captured criminals are then taken to the Hierarchical Public Office of a Hierarchical City, where the vigilante hands over the binding code. If a vigilante is incapable of using Ars Magus, then they can manually immobilize the criminal and either hand him over to the area's officials, or bring the officials to the restrained criminal. However, both of these options will cost money. 
The vigilante system relies on civilian reports. When a crime is reported to the NOL, the NOL creates a wanted poster of the criminal with their face, name, and bounty printed across it. These posters are issued to the Hierarchical Public Offices in each major city and are pinned up in designated areas. For criminals whose identities are unknown, the NOL will disclose the available information to vigilantes, who will then investigate and report back with any extra information to help determine the identity of the criminal. In the case of Ragna the Bloodedge, the NOL officially designated a bounty and issued a warning to those pursuing him.
Grades are also issued with the wanted posters, showing what should be done with the criminal once encountered - this includes apprehending them; beating them to an extent; and in some cases, ending their lives. The grade and the bounty do not necessarily reflect one another, meaning that a low bounty criminal must sometimes be killed and vice-versa. 
A guild for vigilantes exists to help them exchange information on certain targets. Even though the guild's existence is a breach of the Four Vigilantes' Agreements, the guild itself is fairly small and is considered a low priority target by the NOL, so the NOL does not actively pursue it. In some cases, the guild will act as a proxy for a vigilante who has restrained a criminal but cannot collect their monetary reward; in this case, a small fee is deducted.
The profession is considered very dangerous, and individuals have died in the line of duty, but the monetary reward is significant enough for some to justify the work. Vigilantes are similar to, but different from, mercenaries, since they only chase criminals who are wanted by the NOL and do not accept missions from other potential clients such as Sector Seven.
Four Vigilantes' Agreements
1. Obey instructions from Librarium personnel
1. Provide information to Librarium personnel
1. Do not harm civilians, or involve them in danger
1. Do not form organizations
All are numbered one since they are all of the same importance.
- Kokonoe - the first SS class criminal formerly wanted by the NOL. She erased every file they had on her
- Ragna the Bloodedge - the second SS class criminal formerly wanted by the NOL. No longer exists in the current world. Bounty was 90,000,000,000P$, the highest ever recorded
- Arakune 
- Mori P. - Bounty is 2,500,000P$ 
- Doo En Boo Doo - Bounty is 320,000P$
- Young Gang Chaos - Bounty is 160,000P$
- Wild Wiseman - Bounty is 750,000P$
- Miceal Bomber - Bounty is 460,000P$
BlazBlue: Central Fiction Library Entry
This independant armed group was initially formed to deal with the large number of hostile creatures spawned by the influence of the 'Black Beast,' and the collapse of the ecosystem.
Presently, they capture or eliminate people with monetary rewards on their heads, designated by the Librarium. Also known as 'bounty hunters'. Bang and Carl could be considered part of their ranks.
- Four Vigilantes' Agreements
One, obey instructions from Librarium personnel.
One, provide information to Librarium personnel.
One, do not harm civilians, or involve them in danger.
One, do not form organizations.
Vigilantes are obligated to obey these four laws. All are numbered one because they are all of the same importance. 
- Wanted Poster
A document that describes details about a wanted target and monetary rewards. They're mainly used as references by Vigilantes hunting for criminals, but the portrait of Ragna on his wanted poster doesn't resemble him at all. 
- BlazBlue: Calamity Trigger, Teach Me, Miss Litchi! Episode 3 - The Shorty and the Hard Guy
- BlazBlue: Chrono Phantasma Extend, Teach Me More, Miss Litchi! - Tip 2: Continuum Shift Review
- BlazBlue: Continuum Shift, Teach Me, Miss Litchi! Episode 2 - I wanna learn more about vigi-somethings!
- BlazBlue: Central Fiction, Arcade Mode, Mai Natsume Victory Quote Vs Carl Clover, Act III
- Hunts down Ragna for the bounty on his head.
- BlazBlue: Central Fiction, Story Mode, Episode 001, Chapter 001
- BlazBlue: Central Fiction, Library Mode, Character #008
- BlazBlue (manga). Cameo of Mori Toshimichi, the series creator.
- Last four criminals are from wanted posters in BlazBlue: Alter Memory, Episode 1
- BlazBlue: Central Fiction, Library Mode, Organization #037
- BlazBlue: Central Fiction, Library Mode, World #005
- BlazBlue: Central Fiction, Library Mode, Item #014