The Underworld is the dimension souls travel to right after death. It's only accessible to souls, and it's a complex system of smaller ecosystems that are designed to make people feel comfortable enough to "move on". It's not entirely explained what "moving on" but it's implied that there is Hell, talked about in a flyer, and something better.
If someone desires to enter the underworld and come back alive, they must seek the help of an Ancient One, and let their bodies rest in Earth, while their souls travel through there.
The underworld has it's monarchs: the gods Persephone, also known as Our Lady Underground, and Hades. They made all the rules that exists down there, but both are absent in present day. One apparent rule is that no one responsible in someone's death is allowed to be with the victim. There's a strict policy about Shadeless people, but it's not explained what happens to them.
Structure of the Underworld
The Underworld Meadows
The Meadows is a place of transition that resembles a modern waiting room where souls staying while waiting to be sorted out to their fate, according to their karmic cycle. This place is managed by professionals in a suit and tie that deal with dispatching the souls, take into account the transitions in the Hereafter, and check out the archive with the names and background of the deceased.
Elysium is a sumptuous, richly decorated place that resembles a real estate. This place is home to the souls and shades of the dead, and is likely to be a place where Our Lady Underground used to reside, as one of her portrait is affixed to one of the walls and one of the soul said to Julia and Quentin that Mrs Persephone was usually spending some time at the Elysium.
Although not shown, the existence of Hell is attested by the brochure read by Quentin in the Underworld Meadows. Since when Marina Andrieski was briefly resurrected by Julia and Kady she was afraid to go back into a dark place, it's possible that her soul is confined to Hell.