Customer deliveries of Volvo's first compact crossover, the XC40, started less than a month ago but orders have already topped 20,000 units.

Those are big numbers for the debut of the XC40, and it still hasn't launched in what could be its biggest market: China. Volvo is launching the crossover there this spring at the Beijing Auto Show.

"With the XC40, we enter the fastest growing segment in the industry," said Björn Annwall, senior vice president of strategy, brand and retail at Volvo Cars. "These latest figures show that our customers clearly like what they see."

Volvo now has three crossovers, with the midsize XC60 and larger XC90 completing the lineup.

The XC40 is the first vehicle on the automaker's new compact modular architecture. That platform will underpin all new 40 series models, including electrics.

Volvo announced that it is launching the XC40's global marketing campaign starting today with a new version of the classic song My Favorite Things, with this version recorded by Swedish artist Jennie Abrahamson. The song is available to stream on Spotify.