These days, getting a large handout from venture capitalists is rare. It’s even tougher when your startup needs a lot of cash to compete with Google.

Kosmix, however, has defied the odds. In late October, the plucky startup raised $20 million, led by Fortune’s parent company Time Warner (TWX), by assuring investors that Google is not the only way to search on the Web. Kosmix says it takes a new approach to searching by categorizing everything by broad topics for those times when you don’t know exactly what you’re looking for.

“This reflects the fact that Kosmix has a unique technology that’s working well,” said Jonathan Miller, the former chief executive of AOL who is on Kosmix’s board. “No question it’s a difficult period to raise significant amounts of money in a late-stage round.”

A powerhouse of investors are banking on a future where search will evolve beyond typing in specific keyword terms on Google. Former Motorola CEO Ed Zander, who launched the popular Razr mobile phone, recently joined as a private investor and advisor to the company. The Mountain View-based startup, which has raised a total of $55 million in three years, is also backed by Amazon (AMZN) cofounder Jeff Bezos and Legg Mason fund manager Bill Miller.

Miller recently made noise for reportedly raising money from private investors to buy Yahoo (YHOO). Miller, a one-time Yahoo board nominee, refused to talk about Yahoo. He discussed the need for companies like Kosmix to take search to a new level in a way that Google (GOOG) does not. As CEO at AOL, Miller had tried to acquire Kosmix, cofounded by veteran entrepreneurs Venky Harinarayan and Anand Rajaraman. “How do you create breadth and depth in content pages and make it a satisfying user experience is a big and hard problem,” Miller said. “Kosmix has firmly established the lead in how this is going to happen.”

Take the phrase Mount Everest as a topic. Without more search keywords, Google broadly targets what you may be looking for. Google’s first three links include an empty graphics box from Google Maps, a Wikipedia entry, and a well-regarded news site for mountain climbers. The same topic on Kosmix returns a rich summary from Web 2.0 sources. Kosmix includes a short paragraph from Wikipedia along with photos from Flickr, videos from YouTube and video search engine Truveo, forum posts from trekkers seeking climbing partners to Everest, and top mountaineers who’ve climbed Everest.

Rajaraman insists his startup is not another search engine trying to take on the search giant. Google’s competitors – from tiny startup Cuil to software maven Microsoft (MSFT) – are struggling to make a dent in Google’s growing dominance in search despite spending billions. The approach, Rajaraman says, is to deliver relevant results with blogs, videos, pictures and news on a single page.

“We consider ourselves an explore engine. When you don’t know what’s interesting or know enough about a topic, you come to us. We’ve built algorithms based on topics that lead to a very different end point,” he said. “Google’s algorithms are about finding the best Web pages out there. It’s really, really hard to mess with that.”