Atlantis
Atlantis is the sunken city of mythology that is closely linked to Aquaman in all his incarnations.
Golden Age
In the original origin of the Golden Age Aquaman, his father discovered ruins that he believed were Atlantis and learned secrets from them. Those secrets allowed him to turn his son into Aquaman. Aquaman then used a palace in the ruins as his base of operations. The location of the ruins was never revealed, and the evidence of where it was located is contradictory.
Eventually, the Golden Age Aquaman ran across some living Atlanteans. They existed in a domed city and were air-breathers. Because of the war on the surface world, Aquaman tells the survivors that they are better off underwater, and that's the last we see of them.
In a later story, Aquaman takes a picture of the ruins of Atlantis. At this point in the Golden Age, his origin is completely de-linked from Atlantis. But that changed completely when Aquaman enters the Silver Age.
Silver Age
Aquaman's Silver Age origin revealed the location of Atlantis to be where the US Navy planned to test some bombs. Aquaman hadn't visited the city at that point, but his mother came from there. He knows enough lore of the city to recognize both Lisa Morel and Aqualad as exiles. He even attempts to return Aqualad to Atlantis.
Aquaman's first entry into Atlantis is in response to a distress call from the city, which was conquered by aliens from another dimension. After freeing the city, Aquaman and Aqualad are considered the official ambassadors of Atlantis to the outside world.
Aquaman later returns when Atlantis is threatened by odd explosions on the sea floor. The explosions are volcanic in origin and no real threat to the city.
In another event, sea beasts from Atlantis start to cause havoc on the surface world, and Aquaman learns that a villain named Poxomis has taken over the city. Aquaman and Aqualad help to restore order, and return to super-heroing.
When Aqualad gets sick, Aquaman takes him to Atlantis for healing, then sticks around to attend a wedding. When Aquaman is injured, Mera and Aqualad take him to Atlantis as well. Aquaman goes slightly insane and thinks he's the king and Mera is his queen. The Atlanteans humor him for fear that his injuries will get worse if they try to snap him out of it, but Aquaman turns out to be a tyrant and Mera restrains him. The Atlanteans exile him into a "lake of dense water" that he cannot escape from without help. He does escape, with the help of his finny friends, and returns to Atlantis sane again.
Later, when the Atlantean leader Juvor dies, Aquaman is elected to take his place as king. Aquaman reluctantly agrees, but is immediately told that he must take an Atlantean wife. While Aquaman leaves the city to think about it, a tyrant from Mera's world, Oceanus, takes over. Mera, rejected by Aquaman, rules at Oceanus' side, but due to her love for Aquaman she frees the city. She is declared an Atlantean and marries Aquaman after all.
Because Aquaman doesn't take her on his patrols, Mera gets bored in Atlantis and causes all kinds of trouble, including bringing people and pets from her own dimension that take over Atlantis. An old friend, Nikkor, drugs Mera, declares himself king and sells the Atlantean people into slavery. Aquaman helps them escape, and the mob returns to Atlantis to overthrow Nikkor and Mera, tossing them into the Dungeon Depths. After Aquaman rescues Mera and explains that she was drugged, the Atlanteans accept her as queen again.
Aquaman becomes a giant during one adventure, and moves Atlantis from its former location to a deeper and safer spot.
Aquababy is exiled from Atlantis shortly after his birth because of the danger from his powers, but is allowed back in when the powers fade for a time. Later, Aquababy is aged unnaturally by Tamerkhan, who takes over Atlantis. The Aqua-family overthrows the conquerors and Aquaman becomes king again. Aquababy is declared king when Aquaman and Aqualad disappear, and a visitor to Atlantis names Dr Starbuck becomes regent. Dr Starbuck leads the Atlanteans in attacks against the surface world, while disabling Mera with drugs (again!) to prevent her from stopping him. Aquaman and Aqualad escape from the Dungeon Depths and return to Atlantis to overthrow Dr Starbuck and prevent the war from escalating.