One of the bugbears of perfect binding (well, more accurately of reading a perfect bound book) is the tendency of the book to want to stay shut, to mouse-trap. Unless you crack the spine — unsurprisingly something that I hate to do (as someone who’s spent so many hours trying to get these objects made perfectly, I seem to aim for my having read a book to remain undetectable to the next reader) — most paperbacks and many hardbacks will try to snap back. This is because the pages are glued to the cover all down the spine (or in the case of a hardback to a liner, more flexible than a paperback cover but still a force for rigidity) and the cover just doesn’t want to stay open unless you break the spine bond by cracking the book wide open. Cracking the spine will of course encourage pages to fall out. Printing the book cross-grain will exacerbate the mouse-trapping problem.
Ota-Bind picture from Edwards Bros. Malloy.
The generic name for the Ota-Bind solution to this problem is lay flat binding. (Should of course be lie flat, but that ship appears to have sailed a long time ago.) Ota-Bind, which was first patented by a Finnish firm, Otavia, in 1981, works by in effect applying a second mini-cover before putting on the main one, so that the individual pages are affixed to the inner, flexible cover, not to the cover proper. The cover proper is not glued in the spine area so that the pages of the book can rise away from the cover when the book is opened. Given this extra step Ota-Bind does cost more than basic binding, but for many books this stay-open-ness is important enough that the cost is justifiable. Things like lab manuals have to stay open — you can’t be diving for the book as it closes while you are working with a bunsen burner — and Ota-Bind will probably be cheaper than Wire-O, or plastic comb binding. A good discussion of the method can be found at Hyphen Books. RepKover seems to have been an early trade name for the process in USA — why do we persist in these idiotic misspellings in trade names?
The Oxford hollow is another way of encouraging a book to lie flat, but like almost everything else, because it costs more and slows down the binding process, it is only used in the most de-luxe situations, e.g. leather bound bibles.
For other styles of binding search “binding styles”.
Making Book 
[…] and appear from the video at their creators’ website (linked to above) to be bound by the Ota-Bind method so that they lie open. I do think this is an important innovation; and we thought a book was […]
[…] Ota-Bind provided a methodology for lay-flat binding. Peleman Industries now introduces a machine, the V Twister Lay-Flat Paper Converter, which by bending a double fold back and forth allegedly breaks down the bonds between fibers in the paper at the fold allowing it to relax in the open position. Sounds good — the proof of course will only be known after someone serves up the pudding. It is an extra step, and unless you can integrate it into your binding line, would interrupt the binding process. […]