I asked this question some time ago, and after a while I figured out more specifically what I want to ask.
The medusa has the Petrifying Gaze trait:
When a creature that can see the medusa's eyes starts its turn within 30 feet of the medusa, the medusa can force it to make a DC 14 Constitution saving throw if the medusa isn't incapacitated and can see the creature. [...] Unless surprised, a creature can avert its eyes to avoid the saving throw at the start of its turn. If the creature does so, it can't see the medusa until the start of its next turn, when it can avert its eyes again. If the creature looks at the medusa in the meantime, it must immediately make the save.
How does the medusa's Petrifying Gaze work?
The gaze attack specifies that anyone that can see the medusa's eyes is affected, but does the medusa have a "cone of vision", or 360° vision? I'm asking this because the game doesn't really deal with that bit, and I've always run - and seen the game run - with 360° vision for the PCs, so maybe it works the same for monsters.