Average layman here. Assuming the latest generation of planes/avionics rolling out of the factory today, how autonomous are commercial passenger jets? Obviously, autopilot has been around for decades, but what are the limits of its capabilities? Can it take off and land by itself? What can be done remotely, if anything?

Watching a typical airliner-crew-is-dead-what-can-we-do-now movie caused me to think of this question.