George Clooney knows he’s one of the biggest stars in the world — but that doesn’t mean it’s always a good thing.

This week, the Catch-22 actor appeared on The Hollywood Reporter‘s Awards Chatter podcast, where he opened up about his launch to stardom and life in the public eye as husband to Amal Clooney and father to their twins, Ella and Alexander, who turn 2 next month.

In the candid interview, George, 58, spoke about being concerned for his children as Amal, 41, prepares to bring charges against ISIS to the French courts.

“Everything changes when you have two kids on how you have to protect them,” he shared. “My wife is taking the first case against ISIS to court, so we have plenty of issues — real, proper security issues — that we have to deal with on a fairly daily basis.”

“We don’t really want our kids to be targets, so we have to pay attention to that,” George added.

RELATED: Amal Clooney Urges Action over the Maldives: ‘The Noose Around Free Speech Is Tightening by the Day’

Amal, a human rights attorney, asked the United Nation’s Security Council in April to prosecute Islamic State extremists in Iraq and Syria for rape and other sexual acts of violence, according to the Associated Press.

Acknowledging that they may not be able to prevent the crimes entirely, Amal requested that the council at least “punish” the extremists and give some sort of justice to the victims.

The council cast a German-drafted 13-0 vote, with Russia and China abstaining, the AP reports. The final resolution eliminated proposals to give survivors of rape and abuse “sexual and reproductive health care” as a way to avoid a veto from President Donald Trump‘s administration.

It also got rid of a positive reference to the International Criminal Court’s work in charging those believed to have committed the sexual crimes in conflict areas.

RELATED: Amal Clooney Speaks Out in Support of Imprisoned Leader Known as the ‘Mandela of the Maldives’ in New Video and Essay

In addition to the charges against ISIS, Amal has also been involved with a human rights case defending former Maldives President Mohamed Nasheed.

For three years, she continued to defend Nasheed, whom she felt was wrongly imprisoned by a government that has a dangerous disregard for human rights and the democratic process.

Nasheed’s sentence was eventually overturned in 2018 by the Supreme Court.

George went on to say on the podcast that his celebrity sometimes comes with a cost.

“I miss some of that [anonymity]. My wife and I wanted to walk our kids in Central Park, and that’s just not possible,” he explained on the podcast. “We tried, but we walk out the door and everybody surrounds them. And there’s a bounty on my kids’ head for a photo, so that’s something that we are very conscious of.”

Even so, George said he’s grateful for his good fortune.

“I have a pretty good life, right? I have a beautiful wife and two beautiful kids, and I get to work on things I want to work on, and, I have to say, most people don’t get to do that, I’m well aware of it,” he shared. “We live our lives. We don’t hide in corners.”

RELATED: George Clooney Says Amal Banned Him from Motorcycles After ‘Bad Accident’ While Filming Catch-22

One particularly great thing in George’s life right now, besides his family, is the release of his new Hulu miniseries Catch-22which premiered on the network on May 17.

In addition to acting in the remake, which also co-stars Christopher AbbottKyle Chandler and Hugh Laurie, George directed it. Abbott, 32, plays the main character, John Yossarian, while Chandler, 53, plays Colonel Cathcart.

The story is told through the eyes of Yossarian — a divergence from Heller’s original novel of the same name, which famously describes events from the point of view of different characters. Yossarian is a U.S. Army bombardier stationed off the Mediterranean coast in the early ’40s.

“This is a tough nut to crack — famously, one of the toughest nuts ever to crack,” George said on the podcast. “But, given six episodes, you can get to know the characters, and if you get to know them, when they die, it matters.”