Taylor Swift and Tom Hiddleston's romance is heating up.

After going public with their relationship about one month ago, Swift and Hiddleston traveled the world and met one another's parents, and according to a source, they looked completely in love as they took in the sights of Italy, Tennessee and the U.K.

"Taylor and Tom are smitten and look completely in love," an insider shared with E! News. "They walked up to an outdoor terrace where they embraced and spent several minutes kissing. Taylor held Tom close and then he threw his head back with laughter after kissing her."

"The two were very romantic, holding hands throughout their stroll around the Coliseum. They looked very much in love," an onlooker revealed. "She was wearing a pretty yellow sundress. It looked almost vintage, Audrey Hepburn-style with spaghetti straps. He looked dapper in a white shirt and dark trousers...They kissed when they were inside the Coliseum. It was so romantic."

"They took snaps of each other, they chatted and were very taken by each other. It was as if no one else was there yet there were loads of fans and passersby surrounding them," a source added.

As for what Swift's longtime best friend thinks of her romance with Hiddleston, a source claimed last week that she was totally on board and supportive.

“Selena has met Tom and loves him. He is so nice, so fun and a real honest person and the ultimate gentleman,” a source close to Gomez told Hollywood Life. “She likes how he treats Taylor and how he makes her feel, she signs off on him completely! He’s just a real genuine guy and Selena really enjoys seeing that.”

Although Hiddleston has met Gomez, likely at her concert in June where he and Swift were seen getting close, Hiddleston hasn't met all of Swift's friends.

“Right now though she wants him all to herself, considering he will be out of the country working on his new film (Thor: Ragnarok) in about a month," the source explained. "She knows she will have plenty of time in the future to introduce him to her closest friends."

Tags: Taylor Swift Tom Hiddleston