Yixing, mostly, and related teapots. Woefully confused by surfing around the forums, though if I started taking notes I'm sure it would help. I suspect my tuition may be high, though, as there isn't really anywhere around here (that I know of) to find that sort of thing in person (though I have yet to venture into Chinatown).
Also Cha Dao (http://www.wikicha.com/index.php/Cha_Dao_Tools
)... they're for sale all over and their use is described, but I don't really see their use in many videos and so on. Particularly interested in the cup-washing step. I'm sure I could find videos on YouTube, but I risk finding things like Mr. Sleeves.
I thought I knew how to use a gaiwan just fine until I got my first non-TeaGallery gaiwan... and its thicker clay and odder shape is still a little awkward for me to manipulate. I think that's just me, though.