I’ve looked at some info on BSP trees, and a bit on OCTREES, but am a newbie to the whole business. If I would like to have transformable terrain in some future game, what scene organizing technology should I be looking at, and where can I find good tutorials on how to learn/use them?
Thanks much 
What do you mean by “transformable”?
BSPs and Octrees are space subdivision schemes. These help you quickly find what geometry is relevant from a particular point of view and quickly cull irrelevant geometry.
If you want to know what is state of the art for terrain rendering these days, well brute force is actually quite popular for small meshes For larger meshes, look up CLOD - chunked level of detail by Thatcher Ulrich:
http://tulrich.com/geekstuff/chunklod.html
Algorithms of that ilk seem to be the best current options, but “best” for terrain rendering is a slippery term as everyone has different requirements which may effect what is good for you (how are you texturing, is the data static or generated on the fly, the assumptions you can make about viewpoint translation and rotation speed - indeed, whether you can rely on frame coherance at all)
Good luck. My advice would be to go for the simplest thing that might possibly work - you may find that it does
I should have included this link:
Probably the best starting point for any research on terrain rendering.
I think the postee meant deformable terrain.
i.e. Magic Carpet
I’ll try to be more clear What I want to know is how games keep track of polygon info so that objects in the game can have their shape altered. When I looked at a bit of info on BSP Trees, it clearly stated that the world had to be static, so I was looking for some alternative.
For example, some polygon managing technique where you could dig a hole, pile the dirt beside the hole, and then not be able to walk through the pile.
All I know about 3D graphics is what little I have learned from the early chapters of the Red Book, so give me a break if these seem like dumb questions!