In the first quarter of 2016, Huawei sold 10 times as many phones as Apple in Finland, according to research firm IDC. And in October it soared ahead of Samsung for the market-share lead. ... Today you can’t stride through Helsinki without encountering a Huawei billboard. You can’t watch Jokerit, one of the country’s top hockey teams, without seeing Huawei’s flower-in-bloom logo. And you can’t find an electronics store where Huawei’s phones don’t outnumber Samsung’s and Apple’s. ... Enter Huawei—probably the most viable contender yet to loosen the giants’ grip. It’s a 170,000-employee company with $61 billion in sales, selling telecom equipment in 170 countries. Since 2014 it has been No. 1 globally in sales of the networking equipment that underpins telecommunication systems, taking the crown from Sweden’s Ericsson. And now its goal is to dominate the market for the phones themselves. It has taken big strides toward doing just that in China and in growing swaths of Europe—helped in those Western countries by side deals with wireless carriers that have not previously been reported.