Hamlet actor Cumberbatch and Farinelli And The King star Rylance are both nominated in the best actor category alongside Sir Kenneth Branagh for The Winter’s Tale, Adrian Lester for Red Velvet and Kenneth Cranham for The Father.
This is Cumberbatch’s first nomination, while Rylance has been nominated eight times and won twice.
Nicole Kidman is in the running for her star turn in Photograph 51, earning her first Olivier nomination.
She is joined in the best actress category by Gemma Arterton for Nell Gwynn, Denise Gough for People, Places And Things, Janet McTeer for Les Liaisons Dangereuses, and Lia Williams for Oresteia.
Girls Just Want To Have Fun singer Cyndi Lauper could find herself returning again and again to the stage, to perform and also – perhaps – to pick up some gongs of her own.
Kinky Boots, with lyrics by the Grammy and Tony Award-winning singer-songwriter, is up for seven awards, including MasterCard best new musical.
Lauper herself will perform twice during the awards evening at the Royal Opera House in London’s Covent Garden on Sunday, both on her own and as part of a “unique collaboration”, organisers have said.
Best actress in a musical nominee Imelda Staunton will open the show with a number from the multi-Olivier Award-nominated musical Gypsy, having received her 11th Olivier Awards nomination after starring as Mama Rose.
Gypsy is up for awards in eight categories, leading the nominations.
Theatre fans will also be treated to performances from all productions nominated in the best musical revival category, including Bugsy Malone, Guys And Dolls and Seven Brides For Seven Brothers.
The casts of Bend It Like Beckham, In The Heights, Kinky Boots and Mrs Henderson Presents will also take to the stage to perform their hit numbers.
Veteran of the...