Here are 2 useful links which explain this feature and have some examples:
http://wiki.eclipse.org/Jetty/Feature/Continuations
http://docs.codehaus.org/display/JETTY/Continuations : see How it works section.

I use the eclipse version org.eclipse.jetty --> jetty-continuation in one of my client's projects and find it a very useful, powerful and reliable.

You can manage: timeouts, suspending a request, completing implementations, resuming a request, initial phase, adding continuation listeners or just handling the requests in a simple servlet without listeners and only by checking isComplete,isInitial etc...