Jamie Hince and Alison Mosshart are now gearing up for festival appearances in Australia and Japan, before heading off to Glastonbury, where they'll play the Other Stage.
The band's fourth album Blood Pressures was three years in the making, after Alison spent 2009 and 2010 recording and touring with The Dead Weather.
The hiatus led to rumours that Jamie would form his own side project. Some reports suggested he'd put together a five-piece band with his fiancee, Kate Moss.
Speaking to 6 Music, Jamie denied the band's existence, saying any five-piece would be formed of "me, Alison and three gospel singers".
"I'd like to find out where the rumours came from," he joked. "Who are the other four people?"
"And are they any good?" asked Alison.
You can hear my interview with The Kills below: