Inside PEOPLE’s Special Grey’s Anatomy Issue Celebrating 20 Seasons of the Hit Medical Drama Series

The Grey’s Anatomy cast is looking back on the show’s unprecedented success and how it became American TV’s longest-running primetime medical drama.

In PEOPLE’s new Grey’s Anatomy special edition, on newsstands Friday, April 19, Ellen Pompeo, Chandra Wilson, James Pickens Jr. and more of the show’s stars reflect on how the series has remained on the air for 20 seasons — and counting.

“To hold the collective attention of our fans for 20 seasons is something I’m immensely proud of and grateful for,” Pompeo, 54, tells PEOPLE.

The actress says understanding the success of the show — which was renewed for season 21 earlier this month and launched two spinoffs Private Practice and Station 19  — is “easy,” explaining, “[Creator] Shonda Rhimes is a great writer. Second, Taylor Swift named her cat after Meredith Grey! Just kidding. It is because of our awesome fans.”

Fans couldn’t seem to get enough of watching the trials and triumphs of OG interns Meredith Grey (Pompeo) Alex Karev (Justin Chambers), George O’Malley (T.R. Knight), Izzie Stevens (Katherine Heigl) and Christina Yang (Sandra Oh) after the premiere in March 2005.

“I remember actors arriving at work shaken because they’d been chased by paparazzi, which felt really weird for a TV show that wasn’t Friends,” Rhimes, 54, recalls. “I always says that if you watched Grey’s every Thursday night, you spend more time with Meredith and Cristina as your friends than you did with anybody else in your life.”

Wilson, who has played Dr. Miranda Bailey since the beginning, adds, “[Early on] fan interactions would have to come from the mail that would show up at the studio. And that was how you knew that somebody was relating to the character, and then you send back a note. But with social media, there was the immediacy of being able to talk with the fans and hear what they’re personally interested in.”

Rhimes and the cast saw that the real-life impact of the show’s storylines. Camilla Luddington, who has starred as Jo Wilson since season 9, explains, “After ‘Silent All These Years’ [the season 15 episode about sexual assault] aired, within the first 48 hours of that airing [calls to] RAINN’s sexual assault hotline that we gave the number out for increased by something like 43 percent.”

“To see that effect in the real world after we play these storylines out feels so powerful and incredible to be part of, but when we’re shooting it, I try not to think about all the eyes watching and just be in the moment,” she adds.

James Pickens Jr, who plays Dr. Richard Webber, shares, “I’m most proud of how we look at Webber’s whole alcoholism thing. The writers did it in a way that was so respectful, and it was able to resonate with a lot of people. I still have to this day folks who will come up and say, ‘I’ve been in the program, and your character was very inspiring for me.’”

The show also sparked women to follow in the footsteps of Meredith Grey and pursue a career in medicine. “I’ve met women who’ve said, ‘Grey’s Anatomy made me realize that I could be a doctor,’” executive producer Betsey Beers says.

“That people watch the show and then lots and lots and lots of young women went into science is incredible to me, and I think that it’s such a gift that’s given back to me,” Rhimes adds.

For more on Grey’s Anatomy and its cast, pick up PEOPLE‘s special issue, out Friday.

PEOPLE’s Grey’s Anatomy special edition issue hits newsstands Friday, April 19. The magazine retails for $14.99. Grey’s Anatomy airs Thursdays at 9 p.m. ET on ABC.