The Black Market Auction House is a special AH that allows you to buy items that are rare and sometimes unobtainable with gold otherwise. It's an extremely effective gold sink, but it's tucked away in the middle of nowhere, and you can't see what's for sale on your realm from the remote AH. Unfortunately, since Blizzard doesn't make the BMAH accessible through the same API as the regular Auction Houses, you are expected to log in and travel to the Veiled Stair in order to see whether there was anything there for you.
The Undermine Journal is a website that collects, organizes, and displays information about the Auction House of every realm: Horde, Alliance, and Neutral. Additionally, starting in January, they launched a (still beta) feature that shows us the contents of the BMAH. Assuming you're not on a PvP realm, you can avoid the flight to the Veiled Stair to check whether there's something worth buying by simply checking the Undermine Journal.
No PvP realms?
As I mentioned, the regular Auction Houses can be downloaded from Blizzard through an API. This is basically a feed that allows a program to request a complete copy of the entire AH. Part of the design of the BMAH seems to be having it a little bit farther away from the beaten path, though, and as such it's not included with that data. The Undermine Journal's solution to this is to use level one "reporter" characters parked in front of the BMAH on each PvE realm which log in once an hour to check the contents and report them to the site's database. Before Blizzard had this API auction feed, the Undermine Journal used to use a similar strategy to grab the regular Auction House data. An unfortunate side effect of this method, though, is that it doesn't work for PvP servers. It would seem that PvP players like to kill the level one reporters, and there's no easy way to get them back to their spot from the graveyard.
If you're on a PvE realm and stalking the Black Market Auction House for some of the high end PvP or heroic raiding gear, pets, mounts, or old transmog set pieces that pop up there, remember to bookmark your realm's Undermine Journal page. Alternately, you can follow the main Twitter account for the Undermine Journal. Every time the site sees a new item on the BMAH, it tweets it to the realm account (like @drenden, for me).
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