Chinese e-commerce company Shein took the top spot as the most downloaded app in the United States in May, according to a report from intelligence firm Marketplace Pulse. The fashion giant outperformed TikTok and Instagram on the Apple App store and was far ahead of Amazon.  

Since 2015, Shein has become a leader in its industry, initiating a new era of fashion experts call "real-time retail." 

"What Shein has done is, it has established a new norm, which is real time," Allison Malmsten of Daxue Consulting told CNBC in an interview.  

"It is very fast, and the products are updated much more frequently and at a higher volume than any other fast fashion brand." 

But its name has also been marred by trademark infringement allegations and questions about the sustainability of its manufacturing process — controversies some experts say could threaten the startup's investment prospects.  

"If it wants to IPO and if it wants to gather investments, then it really has to come clear and people really need to have peace of mind about what is happening at the company," Malmsten said. 

Watch the video above to learn more about Shein's rise, successes and challenges.