[3][4] A graduate of Yale University, Strong continued his acting studies at both the Royal Academy of Dramatic Art in London and the Steppenwolf Theatre Company in Chicago.

That same year, Strong received praise for his portrayal of Roy Cohn in The Apprentice, which earned him nominations for the BAFTA, Golden Globe and the Academy Award for Best Supporting Actor.

His mother is of Irish descent, and his father's family is Jewish, originally from Russia; his paternal grandfather worked as a plumber in Queens.

Since his parents could not afford to go on vacations outside the Boston area, they put a canoe on cinder blocks in the family's backyard; Strong and his brothers would often sit in it and pretend to take trips.

[2] Strong particularly idolized actors Daniel Day-Lewis, Al Pacino, and Dustin Hoffman—all famous for the lengths they went to preparing for roles—putting posters of their films on his bedroom wall and avidly following news of their careers as well as reading every interview they gave.

Strong worked on the sound crew for Amistad, holding a boom mike over Anthony Hopkins as he made a speech, and he helped to edit Pacino's directorial debut Looking for Richard.

[10] On his first day in class, he found the professor's discussions of Konstantin Stanislavski and accompanying blackboard illustrations so alienating that he decided immediately to change his major to English.

Strong described it as a state of "gilded squalor" in the words of Francis Bacon, with little but his bed, books, and a closet with expensive clothing.

When not working he persuaded local FedEx offices to give him some free envelopes in which he put headshots and recordings of himself performing monologues to distribute to talent agencies.

On set, he was so devoted to attending to Day-Lewis, who lived apart from his family during the shoot, that crew members nicknamed him Cletus after the character from The Simpsons, for his focus on menial tasks.

He became friends with all three actors, and for intermittent periods in the late 2000s, he lived in the basement of Williams' townhouse in the Brooklyn neighborhood of Boerum Hill when he could not afford his own apartment.

At night, he performed the role of an alcoholic Irishman in a one-man Conor McPherson play in a small bar in Midtown Manhattan.

Rooney described his performance as "intense" noting, "while [the] dramaturgical shortcomings hamper the actors...Strong has emotional impact in his single scene.

[13] He was chosen as the 2008/2009 Leonore Annenberg Fellow by Lincoln Center Theater and nominated for the Lucille Lortel Award for Outstanding Lead Actor twice within a three-year period.

[26] Justin Chang of NPR wrote, "Strong is terrific — and very un-Kendall Roy-like — as Paul's father, a plumber with a big heart and a fierce temper".

[27] In 2024, Strong returned to Broadway in the Amy Herzog adaptation of the Henrik Ibsen play An Enemy of the People directed by Sam Gold.

[28] He won the Tony Award for Best Actor in a Play, for his role as Dr. Thomas Stockmann, a principled doctor who attempts to alert the public that their town's spa water is contaminated.

[29] He next portrayed Roy Cohn, a ruthless lawyer and mentor to Donald Trump, played by Sebastian Stan, in the biographical drama The Apprentice which premiered at the 2024 Cannes Film Festival.

[34] Like his idols Daniel Day-Lewis and Dustin Hoffman, Strong prepares intensely for his roles, often to replicate some aspect of the character whether or not it is prominent in his portrayal.

In the first season of Succession, Kendall had to run a considerable distance to be present at an important corporate board meeting after his limousine gets stuck in traffic.

Because Strong wanted to be genuinely sweaty and breathless in every take, he ran as fast and far as he could in Tom Ford dress shoes and fractured his foot.

Two seasons later, he jumped off a 5-foot-high (1.5 m) platform, wearing Gucci shoes while filming the episode "Too Much Birthday",[36] impacting his tibia and femur and requiring a leg brace.

Strong seldom rehearses, saying he wants "every scene to feel like I'm encountering a bear in the woods", an approach he admits may not be popular with his costars.

[39] During the shooting of The Big Short, Strong similarly reduced the interactions with his cast mates, although he admitted to having a good time, he also found it to be "distracting" and "depleting," recalling, "These guys can all be in a comedy, but I need to feel like I’m in a global warming catastrophe documentary.

He quoted jazz pianist Keith Jarrett to explain his approach to acting: "I connect every music-making experience I have, including every day here in the studio, with a great power, and if I do not surrender to it nothing happens".

[9][41][42] In 2016, Strong married Emma Wall, a Danish psychiatrist; they had met four years earlier at a party in New York during Hurricane Sandy.