Most Hollywood couples have no problem being in the public eye, but Gwyneth Paltrow and Brad Falchuk are happy keeping their two-year romance on the down-low.
“She’s crazy about Brad,” a source close to the actress tells PEOPLE. As for wedding bells, the source notes that she’s “cautious about marriage” and “very happy with how things are” — but it’s still “not out of the question.”
Although the actress first met the Glee co-creator when she guest-starred on the show back in 2010, the duo have been dating since August 2014 after Paltrow split from Coldplay frontman Chris Martin after 11 years of marriage.
Instead of flaunting their relationship on the red carpet or flooding social media with cute selfies, the couple flew under the radar when they started dating. However, they have remained by each other’s sides, enjoying romantic getaways and fun outings as a low-key couple.
The longtime pals reportedly vacationed together in Utah before sharing several “fun, flirty” meals over fried rice, baby octopus and beer at Vietnamese restaurant East Borough in Culver City, California, an observer told PEOPLE in 2014.
“They were very friendly and sat at a communal table,” said the observer. “Gwyneth looked pretty with very little makeup. She seemed very comfortable with Brad. They definitely looked like they were on a date.”
They “seemed very happy together,” a source told PEOPLE.
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In May, the couple attended a screening of Paltrow’s mom Blythe Danner’s film I’ll See You in My Dreams in London. As they watched the movie, they held hands and Paltrow rested her head on Falchuk’s shoulder. When the screening was over, the two shared a kiss.
That summer saw the pair jet-setting to Rome. They were spotted driving from the airport to a hotel, and Falchuck “sweetly helped [Paltrow] drive through town,” a source told PEOPLE.
“They were serene and pleased in each other’s company, happy,” the source said.
The Italian getaway continued in Positano, where the Goop founder and her producer beau were photographed soaking up the sun on the Amalfi Coast.
A month after the duo attended the premiere of Falchuk’s show Scream Queens in September 2015 – where the co-creator walked the red carpet solo but didn’t leave Paltrow’s side once meeting inside – Falchuk told PEOPLE the relationship was going “very great.”
“She’s awesome. That’s what everybody loves about her,” he said at an American Horror Story: Hotel event in Los Angeles, adding that his girlfriend wouldn’t be making an appearance in the horror series.
Paltrow and Falchuk started off 2016 with a country-hopping winter getaway. First, the couple were spotted spending time at the beach in Mexico with the actresses’ two children, Apple, now 12, and Moses, 10. Then the duo jetted off to cooler temperatures, landing in Austria before settling in Paris for the week.
Paltrow shared a picture of herself touring around Paris, making a stop at the Centre Pompidou standing next to a man who appears to be Falchuk, his back to the camera, as she snaps a picture of the scenic view.
“The view from the top of the #centrepompidou is at least as stunning as the art contained within its walls. What a glorious place,” she captioned the picture.
Paltrow booked the perfect romantic spot for her boyfriend’s 45th birthday party in March 2016.
“Gwyneth had a girls’ night at the restaurant earlier this year and loved it,” a source told PEOPLE of Beverly Hills restaurant Tempura Endo.
“She booked a private table for a few friends to celebrate Brad’s birthday,” the source added. “It was just a small, casual celebration.”
For dinner, they ordered several Kyoto-style tempura dishes, including tempura bowls. The party also sampled tea from the restaurant’s tea ceremony room.
“Gwyneth looked beautiful,” the source noted. “She is always very friendly and had fun with Brad. They looked very happy.”
In July, Falchuk shared an Instagram photo of the happy couple sipping on cocktails in Fogo Island, an offshore island in the province of Newfoundland and Labrador, Canada.
“Martinis made with iceberg ice,” he captioned the pic, adding the hashtag #happy.
Earlier this month, Paltrow gave a special shout-out to her longtime boyfriend in honor of his 46th birthday.
“Happy birthday, handsome,” the actress captioned a selfie in which she and Falchuk both sport soft smiles.
Falchuk has two children from his 10-year marriage from his marriage to Suzanne Bukinik, which ended in a divorce filing in March 2013. Meanwhile, Paltrow remains close to Martin, with whom she co-parents their son and daughter.