Aquaman still patrols the depths, rarely seen by surface men. (NOTE, this is the original Aquaman who was mutated by his father, not the Atlantean version).
He is a noted hero and lives in Atlantis with his wife Mera when they are not in her watery dimension. He has had several children. Aquaman's first born, Arthur, was killed by the techno pirate Black Manta. This death caused a breakup of Aquaman and his wife, Mera, and during this period he had a liaison with an Inuit woman, who bore his second son, Korak. Aquaman and Mera reconciled and had a daughter, Melina, who is known as Dolphin and is currently married to Tempest, formerly Aqualad. Their lastborn is Arthur Curry Jr., known as Riptide, who is a member of ISIS.
Aqualad/Tempest is in fact Garth, son of Namor and his lover in the late 40s and 50s known as Namora.
Aquaman killed Black Manta in a fair fight about fifteen years ago. About five years ago Black Manta's armor and equipment were stolen from the Altantean museum they had been put in and now there is a new Black Manta, who calls himself the Son of Black Manta or Black Manta II, harassing the sea lanes. As far as anyone knows, the original Black Manta had no children. This Black Manta was recently captured by Riptide and was revealed to be Korak, his elder half-brother.
Aquaman's a half-brother, Orm, is also known as the villain Ocean Master.
Atlantis stays out of the affairs of the surface world as much as possible. As far as anyone knows, the kingdom is ruled by Prince Namor, who spends most of his time under the waves. Occasionally the world hears of Poseidonis, which has a population of fishmen and mostly communicate by telepathy.
The heir to Atlantis is Garth, the son of Namor and Namora. Garth got to know the surface world by acting as Aquaman's sidekick Aqualad and later as the Titan known as Tempest. He has mastered a number of ancient Atlantean elemental magics.
Atlantis is an ancient city, and not the original home of the current populace. It was built by a forerunner civilization and may in fact be a city of the ancient Cretacians.