How is the airspeed-Mach number transition handled in modern airliners? During the climb phase, how is the transition from constant speed (IAS) to constant Mach number handled? Does the pilot flying have to manually "push the button" on the control panel, or is the transition automatically done by the aircraft? How does the pilot / aircraft know when the transition should happen (i.e., from flight plan?)

I guess it's the same during descent?
Does the pilot flying have to manually "push the button" on the control panel?

It's automatic, with a manual changeover button available to the pilots as shown below (label no. 2).



How does the aircraft know when the transition should happen?

When the target climb indicated airspeed (IAS) equals the target climb Mach number, the changeover takes place, usually around FL260. Likewise for the descent. The target speeds are managed by the FMS and can be changed.

Image shows the FMS CDU.


  (3) Displays computed values or manually entered values for the selected mode.