Google (NASDAQ:GOOG) is without question the king of search engines, dominating at least 85% of search engine traffic in the entire world.

But despite the fact that there are markets where Google snatches up next to all traffic, and that “google” has itself become a verb, there still are places where Google isn’t the big man on campus — and that means opportunities for others.

King Without a Crown

China — and its 500 million-plus lost users — is the most obvious example of a market Google has been unable to crack. The “Great Firewall,” as many call it, has been an issue for Facebook (NASDAQ:FB) as well, since the site is blocked by the government.

Strict control over the Internet has thus given search engine Baidu (NASDAQ:BIHU) nearly 80% of the market share, while Google’s portion has dwindled to the teens. Browser Qihoo (NYSE:QIHU) also is creating its own search engine that could steal more of Google’s dwindling slice.

In South Korea, the story is much the same. Tough Internet regulation and greater amounts of Korean data have given the upper hand to the local search engine Naver, the country’s most profitable company. It controls just less than 80% of the market, followed by Daum.net, which has more than 10%. In fact, Google’s not even the top American outfit in South Korean search — at 4%, Yahoo (NASDAQ:YHOO) controls twice the market share of Google.

Google also has had a slow start in Russia, but censorship isn’t directly to blame. According to The Economist, “Foreigners have been much freer to enter Russia, but have struggled all the same,” since they lacked the local knowledge and language skills to gain a significant foothold.

The Russian search engine market is dominated by in-state Yandex (NASDAQ:YNDX), which controls 60% of the market. Google has been making progress, though, thanks in part to the addition of its Russian-language Questions service added a few years back. Its market share has climbed to around 25% of late, while Yandex’s 60% represents a drop of 4 percentage points.

But while Google has been hard at work clawing away at Yandex, its Russian counterpart is far from rolling over. Instead, it’s been clawing right back — in-state and beyond.

Edging Onto Its Turf

One way Google has built its dominance is by building a strong brand, which means being more than just a search engine in order to be the No. 1 search engine … but two can play that game.

Earlier this month, Yandex took a page out of its competitor’s book by creating its own browser and app store in an effort to maintain its dominance and also bolster revenue via search and display advertising.

The app store is especially cutting-edge since it’s a move to mobile and to e-commerce. At least three handset makers already have agreed to pre-load Yandex’s app store on their devices. The browser, on the other hand, is not yet available on mobile devices, but is expected to be shortly. Norwegian mobile Internet browser-maker Opera (PINK:OPESF), for one, has signed a licensing deal with Yandex to share its technology.

Another move from Yandex rubs salt right into Google’s wounds: The company is the mapping partner for Apple (NASDAQ:AAPL) in the region; Google was kicked from that partnership here in the U.S. when Apple decided to make its own application for iOS 6 and the iPhone 5.

The battle for Russia is important as the country — at least in theory — has plenty of room to grow since its Internet penetration rate lags behind that of most industrialized countries.

Beyond the Russian Border

As bitter as that might taste to Google, it’s only the beginning. Yandex also has plans to debut its new features in several neighboring countries, where it has the same kind of advantage and where the same kind of growth potential exists.

On top of that, Yandex also is explicitly targeting markets where Google is the top dog, as opposed to just maintaining its strongholds. As Yandex founder and chief executive Arkady Volozh put it:

“We are focusing on the markets with Google dominance in search … where they have 90-plus percent market share. We’ll be growing 30% or something next year, but it’s not doubling every year as we used to have four or five years ago. We need to find some new markets, new opportunities. … That could improve our revenues dramatically.”

One target the company specified: Turkey. There, Yandex has snatched up a mere 1% share vs. Google’s near-monopoly — but is hoping to scoop up even more.

Turkey in particular is a coveted emerging market. The country has experienced something of a breakout year this year. Turkish stocks — as measured by the iShares MSCI Turkey Index Fund (NYSE:TUR) — have gained 45% this year, helped by companies like Top 10 Stocks for 2012 pick Turkcell (NYSE:TKC) and its 30% YTD gains.

Search engines could ride the same economic progress — especially considering that Turkey reports the highest online consumption rate of any Internet audience in Europe.

Let the Battles Begin

It’s a classic David vs. Goliath showdown. Google’s $46 billion in cash and short-term investments alone would be enough to buy Yandex almost seven times over.

Interestingly enough, the two companies were founded around the same time — but Yandex didn’t go public until 2010 and only recently started to blossom. Revenues and earnings nearly doubled from 2009 to 2010, then grew another 50% in 2011. That trend hasn’t slowed yet, either; last quarter saw revenues jump 50% to $207.2 million and net income surge 76% to $68.4 million.

Despite such eye-popping numbers and the stocks’ 12% year-to-date climb, Yandex has lost 36% of its value since going public — and still is thickly valued at 30 times trailing earnings. Then again, that’s what to expect from a high-risk, high-potential stock like YNDX taking on the global king’s territory.

You just need to have the same kind of fearlessness as its CEO to jump in.

As of this writing, Alyssa Oursler did not hold a position in any of the aforementioned securities.