In cloud computing, Alibaba is primarily known for its rapid growth in China, where the company has long been the leading player in e-commerce.

But it's no longer just a force at home. In the first quarter, Alibaba surpassed IBM to become the world's fourth-biggest provider of cloud infrastructure and related services, according to Synergy Research Group. It still trails Amazon, Microsoft and Google.

Alibaba is helping Chinese companies that want to expand abroad and also increasingly winning business from large customers elsewhere that are looking to crack the China market, which has long been a challenge for outsiders. Alibaba's website shows that European companies, including InterContinental Hotels Group, KPMG, Nestle, Philips, SAP and Schneider Electric are all clients, as are U.S. customers like digital marketing company Conversant and mapping software provider Esri.

Alibaba and the rest of the world's biggest technology companies are building data centers, staffing up and making acquisitions to handle the surge in workloads as more businesses shift their computing and storage needs to the cloud. Alibaba is second in the Asia Pacific region, behind Amazon Web Services, and is rapidly building out elsewhere.

"This is a game of scale and to be a market leader demands vast ongoing investments, a global presence and a global brand,” said John Dinsdale, research director at Synergy, in the report last week.

While Alibaba is making inroads, it's still way behind AWS, whose market share is holding steady at around 40 percent. But surpassing IBM is a notable achievement.