The flamboyant billionaire, who built a global empire out of a mail-order record business, looks to his daughter for guidance as Virgin tries to keep up with the times.

Ten years ago, Holly Branson was studying to be a doctor. Now, she is being talked about as a future leader of Virgin, the company founded by her father, Richard Branson, almost five decades ago.

For more than four decades, Richard Branson has personified showy entrepreneurship on a grand scale.

After starting a mail-order record business in 1970, he used his marketing savvy and personal brand to turn his Virgin empire into a disparate conglomerate that included everything from mobile phone carriers to hotels and airlines. Along the way, he raced hot-air balloons, started a space tourism company, turned a Caribbean island into a private oasis and was knighted at Buckingham Palace.

Today, at 67, Mr. Branson has not eased off the extreme sports. Between kitesurfing with former President Barack Obama and a monthlong endurance challenge, he is lobbying other business leaders to be more responsible, and working with his daughter Holly as she becomes more involved in the business.

Ms. Branson studied as a doctor before joining Virgin 10 years ago. As a member of the leadership team, she has worked on businesses including Virgin Hotels, and is chair of the company’s foundation, Virgin Unite. She is now working to improve the culture and employee benefits across the company, leading to speculation that she will one day replace her father as the face of the brand.

David Gelles: What was it like growing up with Richard Branson as a dad?

Holly Branson: I would be playing video games at one end of the sitting room while the Rolling Stones were chatting at the other end, and not have any clue about what was going on.

Richard Branson: We worked on a houseboat, and we had one room for the living room, and that’s also where I did all my meetings. So my poor wife had to retreat to the bedroom when we had a meeting. The kids didn’t. They stayed crawling around the room.

Holly: She didn’t have to retreat. She probably chose to retreat.

Richard: But I chose my lady well. She’s Glaswegian and an incredible mom, and very down to earth. Her one and only priority is the kids and grandkids. I suspect I see more of Holly than most dads, which is unusual when you think we’ve got 80,000 people working for Virgin around the world. We have managed to get that balance between working hard and spending an awful lot of time together. And we still do.

David: It’s nice to hear a man bring up the importance of work-life balance for once.

Richard: In America, the way people are treated at companies is despicable. It’s two- or three-week holidays, no flexible working, nobody being able to work from home. The length of holidays are dreadful. At Virgin, Holly has been leading the way in really trying to get that right.

Holly: Well, Dad was doing this instinctively when he was building the business. He was allowing people to work from where they wanted to. As long as you get your work done, it doesn’t matter where you are. And he’s proof that you can build a business from basically being at home all the time.

For the last 10 years, we’ve been really making sure it’s embedded in the business. We tried to bring unlimited leave in the U.K., but it took us 18 months to do it legally, just trying to give people more holiday. Now we do it, and people don’t run out the door. They just feel valued and trusted.