Hit musicals Company and Come From Away tied for the most nominations with nine apiece, while The Inheritance garnered eight nominations, the most of any play.
New musical Six received five Olivier Award nominations, while Ian McKellen has received his 11th Olivier nomination for King Lear. Eileen Atkins, who has previously won three times, is nominated for her performance in The Height of the Storm in the West End.
The Lincoln Center production of The King and I received six nominations, including for both lead performers Kelli O'Hara and Ken Watanabe as well as Ruthie Ann Miles.
The National Theatre's production of The Lehman Trilogy received five nods, as did the recent revival of Summer and Smoke which originally ran at the Almeida.
The Olivier Award winners are announced Sunday 7 April at the Royal Albert Hall, hosted by Jason Manford.