Most airliners are equipped with 3-axis autopilots with many fancy features and couplings to various navigational equipment and extra controls. And most professional pilots use the autopilot just as little as they possibly can, with one or two exceptions.
Some airliners are equipped with auto-land. I will get some disagreement on this, but the truth is pilots prefer to land by hand.
There is a common misconception to the effect that an autopilot can fly an airplane. That really isn't true. What an autopilot is really useful for is to reduce pilot workload in certain high-workload situations like complex holding patterns and during long point-to-point legs. The autopilot automatically does the thousands of tiny little corrections required to keep an airplane headed in the right direction (and at the right altitude, if so equipped) without the pilots having to constantly keep adjusting the course from second to second as atmospheric conditions keep bumping the airplane around, usually almost imperceptibly.
If you could look behind you in an airplane and see the path you have taken through the air with the autopilot engaged, you would see a zig-zag path of many slight corrections the net result of which is the desired course.
So it's good to have an autopilot to reduce fatigue and to allow the crew to fold a map or take a sip of coffee.
But autopilots are tricky gadgets, and require constant monitoring to make sure they don't go wacko or just quit, and take the airplane somewhere you don't want to go. Just because the autopilot is engaged doesn't mean the pilots can take their eyes off the instruments and the view outside, for even a minute.
So yes, autopilots are used, but judiciously, and usually during long legs and holding patterns. But the crew is watching closely. So you don't have to.
Have a nice flight...
retired Boeing 747-400 Captain