Here’s what we know about the pair so far.
They had an ‘instant connection’ on set
While making the thriller Deep Water last year in New Orleans, Affleck, 47, and de Armas, 31, had “an instant connection,” a set source told PEOPLE.
“They had great chemistry right from the start,” the source said of the pair, who play a couple in the movie from Fatal Attractive director Adrian Lyne. “Ben always seemed very relaxed and happy around Ana, but at the time there were no signs of romance. He was very focused on making a fantastic movie. He arrived early and was one of the last people to leave.”
They embarked on a romantic vacation after wrapping Deep Water
In early March, the new couple was spotted vacationing together in de Armas’ hometown of Havana, Cuba, where they visited several restaurants and shops. Affleck, who speaks Spanish, was seen interacting with several fans in the local language.
“Ana was his tour guide and took him to all her favorite places. Ben seemed to love the trip. He was in a great mood and very friendly,” a source told PEOPLE of the trip. “They are definitely dating.”
Shortly after, they were spotted taking a sunset stroll in Costa Rica on another romantic getaway, sharing a sweet moment when Affleck pulled de Armas close to him for a kiss.
Ana de Armas/Twitter
Their quality time has continued at home in L.A.
After arriving back in the U.S. from their trips around Latin America, Affleck and de Armas, who is also starring in the upcoming Bond film, No Time To Die, spent Saturday night together and the actress joined The Way Back actor at his home.
Earlier in the day, Affleck spent time with his three children, whom he shares with ex-wife Jennifer Garner: Violet, 14, Seraphina, 11 and Sam, 8.
Affleck and de Armas were also with each other on Friday in L.A., where he appeared to be helping her house hunt.
RELATED VIDEO: Ben Affleck and Ana de Armas Take Romantic Trip to Havana as Source Says They’re ‘Dating’
Ben Affleck and Ana de Armas Take Romantic Trip to Havana as Source Says They're 'Dating'
A source tells PEOPLE that the pair were seen making out at the airport before they boarded their private jet on Saturday
De Armas has complimented Affleck on his talent
“The first time we read the scenes together, it became pretty clear he was going to do something exceptional with a very complex role,” she said of Affleck. “His character is the engine of the story and requires him to move between tragedy and irony or between realism and the most absurd comedy.”
The actress added: “Not only does he know how to do it with ease, he also manages to surprise you in every shot. His talent is infinite.”