Compie computers are rather small, portable devices that holographically project two screens (as shown so far) that can be interacted with via touch. One screen is larger and upright, acting as the actual main screen, and the other is smaller and acts as a keyboard. The latter is not always projected, possibly in order to increase the viewability of the main screen, or simply to save power to increase battery life. Being wireless, mobile devices with no visible ports, it is currently unknown how these devices are charged. However, Tye's desk seems to have a slot or marking that they place the device into or onto - this could possibly be a charging dock or station.
The screens seem to be selective in what it counts as input - a piece of paper has been shown to be thrown through the hologram without the computer interpreting it as touch input.
Computers owned by the human children and the Compie doctors differ in capability, but it is implied that the features unavailable to Tye, at least, are unavailable because of content restriction rather than hardware or software limitations.
Comparison with real-life devices Edit
Compie computers differ very slightly from real-life human computers in input function; Compie computers do not seem to use a cursor or mouse input of any kind, instead using touch input on the screen. While this type of input setup is possible to create on a real computer, it is not commonplace - this type of input setup is nearer to the newer hybrid computers that can function as a tablet with a detachable or foldaway keyboard. This could possibly indicate that the Compie computers shown so far are really lower-power mobile computers.