What We Do In The Shadows

So, you've heard of the Underdark, and for whatever reason, have decided it's a place you'd like to be.
Reconsider that decision.
The Valley has its problems, for certain: Hyena zombies, megastirges, and Kruin, just to name a few. However these are problems only in so far that the default state of the Valley is reasonably pleasant. There's sunlight, fresh water, consistent gravity, and a whole host of other luxuries that are taken for granted.
The Underdark is somewhat more hostile to life. Some scholars say that it partially overlaps with the Plane of Shadow, and while this is true to an extent, it shows a sort of chauvinist attitude to the Prime Material plane. "Because the rules here are different, we must be on another plane" is a shallow argument, as for all of the firmament with the stars and moons, very little of the Prime Material has gravity, air, and warmth.
What it is, is another world, beneath ours, connected by only a few threads of sense and geography. It's easy to think of great underground caverns full of drow and weird aberrations, but the truth is thankfully more complex. 
First, there's the poorly-translated "Upperdark". These are the passages that connect the true Underdark to the surface. While the start and end of these passages are generally fixed, the passages themselves drift to an fro, like a spider's web in the wind. Some creatures have a knack for navigating these places, others must rely on luck, brute force, and some cruel and unusual cartography.
The passages themselves are relatively safe, when graded on the curve that is the Valley. The constantly shifting terrain means the chance of running into traps or hostile natives is rare, and one need mostly content with unsure footing, and the very real threat of starving to death. What does grow down there (both flora and fauna) is poisonous to most things. Pools of water must be avoided at all costs, because any water that's safe to drink will likely be something's hunting ground.
That's not to say these areas are without use or habitation. In the 4th age, the dwarves built great tunnels through the upperdark, called the Deep Roads. They made great engines of iron and steam to traverse them quickly, for reasons that will be explained in a moment. Some dwarves set up holds down there to maintain these engines, but none survive to this day.
Having traversed these passages, one arrives in the Underdark proper (sometimes called the Middledark by those who value literal translations over the possibility of being any fun at parties). While much of it is caves, there's plenty of areas that are wide, open planes with flat rock above and below. Great civilizations exist here, in spite of the fact that there's very little food or water, among other natural disadvantages.
The Drow are distant cousins of elves. They're cruel and intelligent, and adhere to a strict class system based on the circumstances of one's birth. A drow noble, even a young one, is a match for a dozen of their lesser kind. They also have a kinship with spiders, and can use their dark magics to fuse a drow with an arachnid, creating a kind of spider-centaur called a Drider. Needless to say they're all horrible, nasty, and powerful.
The Duergar are distantly related to dwarves, and respond by loathing dwarves, drow, and anything else. They do build strongholds like the dwarves, and are master craftsmen. They can change their size and opacity at will, making them both surprising and dangerous. Physically they look like their surface cousins, but with pale grey skin and black hair. Possibly in response to the Drow's love of illusions and enchantments, the Duergar are mostly immune to both these things, and are physically resiliant to boot.
The running theme here is that the creatures below are "superior" version of their surface kin. Also in the Underdark are rumored to be other such versions of surface creatures. There's said to be a race of kobolds that are close to their draconic origins, and a race of human-like demigods that breed true. By number, the two largest inhabitants of thew Underdark are the undead and the aberrations. The undead are familiar enough, although they have an intelligence and purpose not often seen on the surface.
Aberrations are an entire class of subterranean creature, that all have one thing in common: They obey slightly different laws of ecology and biology to surface creatures. Most eat, but what they eat and why doesn't make any sense if considered from the sheltered view of nutrition. Some eat emotions, or dreams, or even their own bodies. That said, if you encounter such a creature, it's a fair guess that they'd find you appetizing. They're no better on the inside, having organs and tissues unlike anything seen elsewhere, with functions unknown. For this reason, a stab the the head, or eye, or soft underbelly may not yield the desired results. 
Should one survive all these horrors, there's one level deeper. Very little is known of "The Below", except that it is home to that famous horror, the Illithid. As tall as a human, these creatures are said to subsist entirely on the minds of other intelligent creatures, making them a horror to small children and powerful magi alike. There's many rumors about these creatures, but a popular one is that they're from the future, and somehow exist backwards in time. There are many stories of the Illithid that supposedly date from the 3rd age: When the Gods and mortals fought the titans, the Illithid took the titan's side, and nearly won the war for them.
As mentioned at the start of this, one of the key insights into understanding the Underdark is that it behaves on slightly different rules to the surface. These discrepencies in the physical sciences allow for creations of materials, constructs, and magic that not only can't be found on the surface, it in fact can't exist on the surface at all. It's often said that the black armor of the drown becomes as brittle as a biscuit when exposed to the sunlight. This isn't true, it's just that when taken to the surface, the rules of the underdark come undone, and what was once a tough metal is now worse than scrap. 
It's these bent rules that allowed the dwarves to build their great engines. Should such a thing have been constructed too close to the surface, it would have fallen apart instantly. In the Deep Roads however, the engines worked perfectly.
Possibly the strangest expression of these changes is to magic. Many spells function differently in the Underdark, but teleportation magic does not work at all; this includes summoning and binding rituals. There's no ifs or buts, if you want to move between two places in the Underdark, you must walk, crawl or fly there. While the Gods can reach into the underdark (to grant spells, or notice misdeeds), they're powerless to do anything more, as they cannot summon agents to enact their will.
There you have it. The underdark is cruel, inhospitable, bizarre, and populated by creatures that are all three. Getting there is hard, and getting back may well be impossible. On the bright side, there can't be anything down there of interest. 
So, wait, is the underdark in this campaign? Will we go there?
It is, as Selph's presence indicates. As to whether you'll go there, I can't see why you would. I can't see why it'd come up. Best to put it out of your mind.