The husband and wife dancing pair became front page news after a kiss between Katya and her celebrity partner Seann Walsh.
Seann was at the centre of a tabloid storm during last year's Strictly after he was pictured secretly snogging Katya despite both being in relationships.
While Katya is married to fellow Strictly dancer Neil, Seann was dating Rebecca Humphries, who has since dumped him.
At the time, both issued grovelling apologies and made a sombre appearance on spin-off show It Takes Two.
Now they've spoken out about the drama as they prepare for their own dance show, Somnium: A Dancer’s Dream.
In an interview with the Daily Mail, Neil recalled: "It was a shock. And we had to work it out between ourselves, to understand what had happened.
"But I wasn’t going to allow that one little thing to get in the way of ten very happy years."
He added: "I’m private. I’m also quite positive. I wanted to speak to Katya – we had to sort it out privately."
"Every love story has its ups and downs," Katya added. "No relationship is perfect. I think people can relate to that."
"I apologised when it happened, and I’m happy to apologise again now," she told the publication. "I made a mistake, but I don’t want that one mistake to jeopardise everything we’ve built.
"And it hasn’t. We have our trust back."
Based on their own love story, Neil and Katya's Somnium show tells the tale of a British boy and a Russian girl who fell in love and became World Champion dancers.
It plays at Sadler's Wells in London this June. You can book tickets here.
The BBC confirmed the 2019 Strictly Come Dancing pros earlier this year.
Alongside Neil, the male pros are AJ Pritchard Aljaž Škorjanec, Anton Du Beke, Giovanni Pernice, Gorka Marquez, Graziano Di Prima, Johannes Radebe and Kevin Clifton. Pasha Kovalev won't be returning having decided to quit after 8 years.
The women joining the pro cast together with Katya are Amy Dowden, Dianne Buswell, Janette Manrara, Karen Clifton,, Luba Mushtuk, Nadiya Bychkova and Oti Mabuse.
Strictly Come Dancing will air on BBC One later this year.