I'm sure Wave doesn't poll the server every millisecond to find out if the other user has typed something... so how can I see what the other person is typing as they type? And without hogging the bandwidth.
Persistent HTTP, Comet
Keep your HTTP connection alive and send characters as they are typed
*Edit in 2014: also, take a look at WebSocket and HTTP/1.1 Upgrade header. Browsers started implementing this around 2010, so I'm adding this to original answer.