As The Doctor noted in Dark Water, almost every culture has legends of an afterlife, and throughout this season we have seen Missy and her assistant Seb welcoming various characters to it. But which culture's afterlife is it? Despite Missy referring to it as "The Promissed Land" or "Heaven", it's not any contemporary religion's paradise. "The Nethersphere" is a more apt name, as it seems to based on the ancient Greek Underworld.
The plot of Dark Water parallels the Greek myth of Orpheus and Euridice. Clara takes the role of Orpheus, trying to recover Danny from the Underworld. In some versions of the Orpheus myth, Orpheus is unwittingly responsible for Euridice's death, as the fact that his music tames all wild beasts has left Euridice unafraid of snakes. Clara is unwittingly responsible for Danny's death, since her phone call distracted him while he was crossing the road. Volcanoes are often portrayed as gateways to the underworld.
There were various rivers in the Underworld. The most famous was the Styx, which was notably murky (stygian) - it was dark water. Having been bathed in the Styx was what gave Achilles his famous invulnerability - a power he shares with the Cybermen. Another of them was the Lethe, the river of forgetfulness. Those who drank from the Lethe forgot their former lives, and could then be reincarnated. The chance to forget his former life is what Seb offers Danny, although he doesn't explain that he's planning to reincarnate Danny as a Cyberman.
In the Orpheus myth, it is scepticism that proves Orpheus' downfall. Unwilling to trust Hades (who has never given up one of his subjects before), Orpheus breaks his promiss not to look back, and thus loses Euridice forever. Clara, encouraged by the Doctor to demand proof of Danny's identity, allows him to goad her into cutting off the conversation (ironically by repeating what she was telling him when he died), because he does not want her to risk her own life. We end the episode with the threat that Clara may lose him forever…