Most shoppers have probably heard of Zara, H&M, Uniqlo, Aldi or Lidl, all retailers that ventured into the U.S. after they found success overseas. Now, the number of international retailers — apparel brands, grocers, cosmetics companies and more — looking to move to America is growing at a rapid clip, industry experts have told CNBC. But making a splash in a new country isn’t easy, even for well-established brands. H&M and Zara, for instance, had to pull back on opening new stores as sales rocketed online and foot traffic disappointed in certain cities. There’s often some trial and error involved, as shoppers’ taste preferences vary by market.