Meaning from OED:
Having started and in progress; being done or carried out:
Usage:
Have the phone interviews gotten under way?
This is colloquial English
Have the phone interviews got under way?
This is incorrect
The right usage is:
Are the phone interviews under way?
Usage examples from OED:
recruitment is well under way
The project is already under way, with work due to be completed by early next year.
At one end of this area, a massive building project has been underway for the best part of 20 years.
The doctors' surgery will house five GPs, and moves are underway to recruit a sixth.