The Judgment Pavilion is a place in the Underworld where the dead go to be judged on what location to be sent to in the Underworld. The judges are persons like King Minos, Thomas Jefferson and William Shakespeare.
|“||Cool black tent, though, right?||”|
–Nico Di Angelo, describing the Judgement Pavilion, Percy Jackson and the Olympians: The Ultimate Guide
There are three judges who decide if the person goes into the Fields of Punishment, the Fields of Asphodel, Elysium, or, on a rare occasion, the Isles of the Blest. They seem to be able to enter the mind of who they are judging, and recall their memories to judge them. They are also able to be bartered with, for example when Hazel Levesque offered to give up her place in Elysium to spare her mother the Fields of Punishment.
The neutral souls who haven't done good or bad in their lives are allowed to skip judgment and go directly to the Fields of Asphodel. Souls that have done good deeds in their lives are sent to Elysium; the bad souls that have done numerous evil deeds, enter the Fields of Punishment.
Judges are decided to pass judgement on all souls that enter the pavilion. While it is not shown how these judges are picked, they are normally people that showed great wisdom or fairness in life, such as William Shakespeare. However, these judges can also be cruel, such as King Minos.
Originally, a panel of three living judges determined the fates of mortals in the Underworld right before they died. However, this system proved to be faulty, as the judges were susceptible to the lies and bribes of the people whom they tried. This resulted in evil souls charming their way into Elysium, while the truly benevolent ones were consigned to the Fields of Punishment for not meeting the judges' expectations.
When Hades took over as king of the Underworld, he visited Zeus on Olympus and suggested having the judges be a panel of spirits under his command, making it impossible for them to be influenced. Furthermore, souls would only be judged once they have entered the Underworld proper, where the judges would be able to see through deception and try the dead based on their good or bad deeds. Zeus agreed to this, but only if the judges were all demigod sons of him. Rather reluctantly, Hades complied and appointed Minos, Aiakos, and Rhadamanthys (all former kings), thus establishing the Judgment Pavilion. 
Percy Jackson goes to the Underworld where he sees the souls enter the realms after their judgement.
It is explained that the reason why Daedalus ran into his Labyrinth was to escape death itself. This was because after Minos was murdered, Minos would haunt him in the afterlife. Daedalus eventually decided it was time for him to die and gave his life willingly after the Battle of the Labyrinth, though the other demigods protested that with Minos on the jury, he wouldn't receive a fair trial. Daedalus had faith in the ruling of the judges and asked Nico di Angelo to release his soul. The judges didn't send him to the Fields of Punishment, but instead ordered him to help ease the flow of souls into the Underworld as his punishment, although Minos wanted him to bathe in cheese fondue for eternity.
Hazel entered the Judgement Pavilion with her mother after their deaths. The judges examined the lives of the two carefully. While Hazel had almost caused the rise of Alcyoneus, a son of Gaea, she had done so only because Gaea was manipulating her mother's body. It was decided that Hazel would be allowed into Elysium for sacrificing herself to prevent Alcyoneus from rising, but her mother would be sent to the Fields of Punishment for allowing Gaea to control her and allowing herself to almost become a sacrifice. Hazel, who couldn't allow her mother to be sent to the Fields of Punishment, asked the judges to accept her proposal. Hazel volunteered to be sent to the Fields of Asphodel along with her mother, stepping down from Elysium, but saving her mother from the Fields of Punishment. The judges accepted this compromise and sent them both to the Fields of Asphodel.
|Underworld:||DOA Recording Studios | Doors of Death | Door of Orpheus | Elysium | Erebos | Fields of Asphodel | Fields of Punishment | Hades' Palace | Isles of the Blest | Judgment Pavilion | Persephone's Garden | River Lethe | River Styx | River Acheron | River Phlegethon | River Cocytus|
|Tartarus:||The Mansion of Night | Hermes' Shrine|