The whole laptop rolls up in section. With flexible OLED displays, this is not some distant space-age dream. Typing on a virtual keyboard which also acts as a screen, well, that’s just the same touch-sensitive displays with virtual keyboards that are becoming very common. The laptop opens flat to become a tablet, turns to the side to become a display monitor/screen… these are in fact already the technology of today.
There are a few things with today’s notebooks that need improvement. The most important one has to do with power, and there are two things to it: battery life, and wireless power. Everyone wants the notebook to last as long as possible without having to plug-in. What would be nice to have is a workhorse notebook that can run for 10 to 12 hours. That should be pretty long enough for most practical purposes (e.g. you probably won’t be away from your desk for 10 hours, you probably don’t get 10 hours of notebook use on a flight, etc).
The other thing about power… is that it would be wonderful to have wireless power. Everything that used to be connected to the notebook is now wireless nowadays, except the power cord. I know there are some induction based charging things but they require such close contact (like those of electric toothbrushes) that the whole benefit of wireless power is lost. Wireless power sounds dangerous and perhaps, even, slightly farfetched, but it has been the focus of much R&D. I remember reading about a research lab having successfully demonstrated powering a 60W light bulb from like half a metre away with something like 50% efficiency?