There are many cathedrals in Vienna, but the most iconic and, arguably, the most well-known and important one is Stephansdom (a.k.a., St. Stephen's). Two days ago (2-June) our group went for a tour.

[Note: I did not take this photo (I wish I had!)]

As you can see, the building itself is impressive (the spire is just shy of 450 ft high). The original construction was completed in AD 1160, but repairs, reconstructions, and expansions lasted into the 1500's (it's built of limestone, so, really, there's almost always some repair and/or cleaning of the exterior going on). What's inside the building is equally impressive. Here is a shot looking from the back of the church to the front toward the high altar.
One of the first things that captures people's attention is the stone pulpit that is in the middle of the nave of the church. It is extremely ornate.
As you can see, it's quite gothic in style, matching the exterior of the building. The figures you see on the pulpit are Augustine, Ambrose, Gregory, and Jerome). Going up the handrail are carved lizards and toads, and at the top of the rail is a dog that protects the preacher. Unfortunately, I didn't get a shot of the perhaps the most interesting feature of the pulpit: underneath the rail is carved a man looking out a window—supposedly a self-portrait of the stonemason who carved the pulpit (affectionally known as Fenstergucker [window gazer]). Sorry I didn't get a photo of that, but I did get one of our students gazing at the pulpit.
Also in the cathedral, to the left of the high altar (at the head of the north nave), is Wiener Neustädter Altar (one of 18 altars, by the way), a magnificent work of art with a facsimile of the x-ray of the shroud of Turin along the bottom of it.
This thing is huge! It's 100 sq. meters (or 1100 sq. feet). Though it is much older (made in like 1440's) it was sold to and installed in Stephansdom in 1885. In 1985, its 100th anniversary in St. Stephen's, restoration on it began. It took 20 years to complete and like 1.3 million euros!
Our students (and faculty) are visiting some of the many other cathedrals in Vienna to do a little comparing and contrasting. There are something like 25 in district one alone, so they have plenty to choose from! My personal favorite is Malteserkirche.