Here’s a great screenshot showing off one of the new levels. It’s ten turns into play, so there’s lots of activity going on, and you can also see the nice way that lanterns light up dark spaces. Places too far from the light, or around a sharp corner, will stay in dark bluish shadow. These areas are dangerous, and monsters can appear unexpectedly from any dark recesses!
The best way to keep a tunnel of yours safe from critter infestation is to put lanterns up in areas you control. Monsters hate the light, and new monsters will not be spawned in areas lit up. Ending your turn outside of combat will normally drop a lantern, so you end up dropping off quite a few as you go along. But areas you haven’t reached yet, such as those areas of the Deep you can see at the bottom, will remain in shadow for a very long time. The faster you get down there, the faster you can make them safe, but delving too deep carries it’s own risks.