Last week the Chinese personal computer maker posted another quarter of big gains in revenue and profit — even in markets where PC sales fell. Lenovo has now nearly overtaken its largest rival, Hewlett-Packard (HPQ), as the largest personal computer manufacturer in the world. And while many in the industry are fretting about the soft global PC market and the rise of the tablet, Lenovo remains bullish on, well, computers. “The tablet is a good innovation, and a good compliment to the traditional PC,” said company chairman and CEO Yang Yuanqing in an interview with Fortune. “Some say the tablet will cannibalize the PC. I have a different opinion.”

His view? Consumers will move toward high-end computers and smartphones with a large screen, leaving tablets as an important niche product. The company even has a moniker for the coming age of computing: the PC-plus era.

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Yang’s is one of countless predictions about a fast-changing industry. But in the last three years, his company has proved that it can read the tea leaves better than most. Lenovo has skyrocketed from global 9% market share in 2009 to 15% this year, almost even with HP at 15.7% according to research firm IDC. Its PC shipments rose 24% in the last quarter, the company said, compared with a 2% decline in the industry overall.

Those improbably large gains come largely from increasing sales in underserved markets. For example, last quarter Lenovo reached a record market share of 35% in China, where personal computer ownership rates are about one fifth what they are in the US.. In the US, that number is closer to 100%. The company has focused in particular on rural areas and small cities in China, where PC ownership is lowest. It has more than 30,000 franchise locations in the country. Urban-centric Apple (AAPL), by comparison, has six. Lenovo’s reach is so broad in its home country, that where truck distribution isn’t convenient, it sometimes moves its product via bicycle — or even by donkeys Yang says.

In other emerging markets, the company’s aggressive growth strategy has come at the cost of high profit margins, but has resulted in big sales. Market share is now in the double digits in 35 countries, analysts from Citigroup (CIT) wrote in a research note, up from 12 countries a year ago. The strategy of going into untapped areas has left the company with room to grow, says Yang, even as other companies are facing shrinking demand.

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Another growth driver, Yang says, will be the company’s investments beyond PCs. The company’s new mobile technology division now makes up 7.3% of company revenue, up from 3.6% last year. Lenovo sold 7 million phones in China last year, 5 million of them smartphones. Despite being a relatively new business, its smartphones have snagged 10% market share in China, second only to Samsung. The business is expected to reach profitability soon.

The company has also made a play in the server businesses, announcing plans earlier this month to partner with EMC (EMC) to develop servers for EMC storage units. It expects the deal could bring in billions in revenue in the next several years. In a note to investors Barclays (BCS) analysts wrote that “[Lenovo] has transformed from a PC company focusing only on China and the US enterprise PC segment,” into a diversified company with a hand in emerging markets, consumer products, smartphones, tablets and servers.

But some worry that Lenovo is not immune to the woes ailing the industry. “They’re doing much better than their competitors, but they’re also facing the same environment as their competitors,” said IDC research director David Daoud. “The question is could they continue to deliver the types of results that they’ve delivered. There are a lot of wildcards out there.”

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One of those wildcards is the global slump in PC sales, another is a slowdown in the Chinese economy. China accounts for 42% of Lenovo’s sales. The country’s growth appeared to stutter in July, with exports increasing just 1%, down from an 11% increase the month before. “There is definitely some uncertainty here,” Yang says. One of the primary reasons, he says, is government control over the real estate bubble. The other is that the global economic slowdown could impact Chinese exports.

But Yang added that he thinks neither of those factors would have a lasting impact. “Long-term, I’m still optimistic on the Chinese economy, and the PC market,” he said.

In China, PC shipments declined 3%,while Lenovo’s PC shipments in the country grew 9%. Part of that success, Yang says, is knowing the market. Instead of using donkeys and bicycles to move product to cities off the beaten path, American companies might try to hire a carrier such as FedEx (FDX) to make deliveries at a greater cost. Lenovo also knows how to strategically advertise in smaller Chinese cities, rather than having to rely on an ad company such as Saatchi & Saatchi to navigate the landscape for them, as an American company might.

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Indeed, Lenovo’s advantage in China seems to be that it is a local player that understands its home market but boasts a product that’s sophisticated enough to go toe-to-toe with its U.S. counterparts. (The same could be said for Yang, a 47-year-old Chinese native who arrived at the interview slightly breathless in an open-collared, stylish purple shirt. His staffers call him by his first name, or Y.Y., a practice many Chinese CEOs would not tolerate.) As a result of its local edge, Yang welcomes the competition and says he’ll even explain his playbook on logistics and marketing to rural customers. But he adds: “Even if I told them how to do that, they couldn’t.”