But the road to stardom has not come easily for the 56-year-old classically trained thespian, who, despite his unquestionable talent, was nearly derailed by personal tragedy.
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At the time, Rylance decided to withdraw from his scheduled performance at director Danny Boyle’s Olympics opening ceremony, where he was expected to recite verses from The Tempest.
The passage was ultimately read by Sir Kenneth Branagh, with Rylance later telling The Sunday Times that he found Boyle's staging "very hard for me to remember" under the circumstances.
He noted that the "explosion" in his life caused by van Kampen's death made it hard for him to see "what was going on before."
Rylance also told The Sunday Times that he found himself having conversations with his late stepdaughter following her death.
"That ability to tell when your imagination is receiving something and your imagination is creating something – that's a very subtle difference," he explained in 2013.
What You Don't Know About Academy Award Nominee Mark Rylance
"I'm aware since Natasha's died of conversations with her, which obviously I have a lot of times. I'm aware sometimes in those of when I'm making up the conversation and sometimes I'll have a sense of, 'Oh, why did you say that?' "
While these conversations exist in Rylance's head, they can feel so real as to influence his views on the afterlife.
"In my imagination she'll do or say something that is very, very resonant, so I will feel from that my faith that her soul is still existing somewhere in the universe will be confirmed," he explained. "Then I'll be doubtful that that's what I want it to be. So I swing between doubts and confidence."
Rylance went on to continue his stage work, acting in Richard III and Twelfth Night at Shakespeare’s Globe and in the West End, where he had served as artistic director between 1995 and 2005.
Like many actors do when faced with tragedy, Rylance was able to channel his loss into his performance as Olivia in Twelfth Night.
"One's life has changed, so one brings a different thing to it,” he explained. "Most obviously, more people have died that are close to me in the last 10 years, and so the fact that [Olivia] is in mourning for her father and her brother, I have now a more concrete experience of what that is."
But in 2015, Rylance nearly turned down playing Thomas Cromwell in BBC drama Wolf Hall because he felt that playing a man struggling with the loss of his wife and daughter hit a little too close to home.
"I read episode one and thought I wouldn’t do it. This is something that is just trying to capitalize on what happened to us and get me to act it out; no way; I’m not doing this," he told Radio Times.
"But my wife Claire said: 'Do it; read the book and do it. It’s not the main part of the story. It’s not a badge of honor, defining your life – other people have had their tragedies, just as vital and strong; but all artists use themselves …What else can you do?' "
Rylance would go on to be nominated for an Emmy and BAFTA for the role. "It’s unchartered ground if something tragic like this happens to you. You become aware it has happened to a lot of people. You make your own decisions about how you get through it," he explained.
Now, four years after van Kampen's death, Rylance and his wife Claire are proudly making the red carpet rounds amid his accolades for portraying master spy Rudolf Abel in Steven Spielberg's Bridge of Spies.
For an actor normally content with performing in the confines of the stage, his newly minted status as Oscar winner is sure to catapult Rylance permanently into the mainstream. He'll be back on the big screen with Spielberg's adaption of Roald Dahl's The BFG in 2017.