By JP Mangalindan
October 24, 2012

FORTUNE — The Internet has created a global marketplace unlike anything humanity has ever known: more people connected to more products in more places. So why is accepting online credit card payments such a nuisance?

Stripe, a San Francisco-based startup, wants to simplify the process merchants go through to do so. John Collison, 22, and his brother Patrick, 24, founded the company in 2010 to let companies and individuals quickly accept payments by adding a few extra lines of code to their sites. Stripe processes payments, securely storing users’ credit card information. The company charges a flat fee of 2.9% plus 30 cents of every transaction.

How does Stripe differ from PayPal, the Web’s dominant payments firm? PayPal (EBAY) shuttles customers to a separate Web page and can act as a user’s digital wallet. Stripe, by contrast, operates in the background, allowing its merchants to customize the buying experience to look the way they want it to. Purchasers may not even know Stripe’s services are churning in the background. “We’ve come to accept that starting an online business is miserable, and it just doesn’t have to be that way,” explains the spritely, fast-talking John Collison.

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Stripe emerged from the Collison brothers’ past ventures. Natives of Dromineer, a small village on the shores of Lough Derg, Ireland, Patrick double-majored in math and physics at the Massachusetts Institute of Technology and John studied physics at Harvard. During college, they developed Auctomatic, a management system aimed at eBay power users that they sold months later for $5 million. Another venture was an offline Wikipedia iPhone app. “It was profitable enough for college students,” Collison says.

The brothers discovered the most challenging part of their business wasn’t developing the product but collecting users’ money. Payments via Apple’s (AAPL) App Store were hassle-free. What if, they asked themselves, a service existed that enabled online businesses to handle transactions in a similar way? And Stripe was born. The potential market is massive. Online shopping is growing drastically and, according to Forrester Research, is expected to increase 62% by 2016. The company says U.S. consumers will spend $327 billion online in 2016.

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Stripe’s backers include PayPal co-founder Peter Thiel, Tesla CEO Elon Musk, Sequoia Capital, and Andreessen Horowitz. The company raised $20 million earlier this year, valuing the firm at an estimated $500 million. Stripe won’t break out user numbers, but as of last July, there were 100,000 Stripe developer accounts, with clients such as the Museum of Modern Art, Foursquare, travel site Hipmunk, and the literary journal McSweeney’s.

Super angel investor Ron Conway, also a Stripe investor, has sung the company’s praises. Recent investor and Box CEO Aaron Levie calls the Collison brothers two of the smartest entrepreneurs he’s met. “There are a lot of companies today that aren’t going after really big problems or solving really big issues in big spaces,” Levie says. “Stripe is setting itself apart by doing just that.”

In recent months, Stripe has expanded its services, launching in Canada last September — its first market outside the U.S. — then rolling out Stripe Connect earlier month. Stripe Connect opens the door to more potential users by letting any Web site user like say, a marketplace seller, accept credit card payments. To be sure, the field of companies trying to crack digital payments in a larger sense is vast. (See Fortune‘s cover story The Death of Cash for an overview.)

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The company’s next goal, not surprisingly, is to expand globally.  “When’s the last time you bought something from someone outside the U.S.?” asks Collison. “That’s what really matters — making those kinds of transactions happen friction-free.”

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