There was a different kind of press last year, when, on the strength of new evidence, police re-opened the Natalie Wood case. Walken's one-time co-star drowned in 1981, after an evening drinking with her husband Robert Wagner and Walken on the couple's yacht.
This year, the cause of death was changed from "accidental" to "undetermined.".
"Were you surprised that they reopened the investigation 30 years in?" asked Smith.
"Did you think it was settled?"
"Well, I, no, I - I - I didn't understand that," Walken said.
"Why they opened it again?"
"Still don't, no."
"Have you talked to police about it?"
"Oh, I've talked, you know, over the years I've - I've talked about it. And the truth is that I, I haven't talked about it in 30 years."
"But if they open the investigation again, are they re-interviewing everybody?"
"I don't know," Walken replied. "Let me know what happens."
Over the years, Walken's films have grossed more than $2 billion. But his voice has become a comedic cottage industry of its own.
"A lot of people do it," he said. "My wife says that Kevin Spacey [is best]" Others Walken named include Kevin Pollack and Jay Mohr.
"When people do it in front of me I usually don't know what they're doing right away. I always think, Why are they speaking that way?"
Besides his voice, Walken's other trademark is his hair, which he says he owes to a bit of advice he got long ago.
"I became friends with Tony Perkins, the actor. And he said to me, 'That's some head of hair you got there. You know what you do? You just grab it every morning for five minutes and you pull it forward, just yank it as hard as you can.'"
"So you really pull on it?"
"Every morning. just yank on it! I watch TV and I just - it keeps your scalp loose," Walken explained. "And I've been doing it ever since. And like, you know, I got a lot of hair for somebody who's, you know, 87 years old!"
And now, after a career spent making us laugh and cringe, Walken is poised to make us cry.