Square, known for its tiny credit card reader that allows businesses to process payments from a smartphone, is announcing its latest product today in San Francisco: an iPad app that replaces cash registers and allows customers to pay for products with their Android or iOS devices. Card swipes, signatures and old-fashioned paper receipts need not apply.

“What we’ve done, is we’ve looked to what Amazon (AMZN) has done with 1-click, and what iTunes has done with one click, the fact that the mechanics of payments are no longer there,” Dorsey told Fortune‘s Adam Lashinsky during an exclusive early look at Square’s new features. “You’re no longer thinking about taking your card out and reading off the numbers, all you’re worried about is hitting that one button to buy.”

Half-a-million small businesses have signed up for Square’s service since its 2010 launch. But Square remains mostly unknown to shoppers. The company hopes to change that with its two new features, Card Case for consumers, and Square Register for businesses. Starting today, customers can pay for purchases using their smartphones at any of Square’s 50 launch partners.

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Here’s how it works: you order a coffee at a participating shop, for example, and when you swipe your credit card, the receipt is emailed to you. Leave your card on file with Square, and next time you visit the coffee shop you can browse the menu and pay with the company’s new app by pressing a button. They call it opening a tab, a high-tech homage to the pad-and-paper accounting that barkeeps, druggists and general store clerks were accustomed to many generations ago.

Square’s business customers are a hodge-podge of food trucks, hairdressers, small retailers and restaurants. Aside from the company’s card reader that elegantly plugs in to the headphone jack on your iPhone, the service’s appeal lies in its simple software and its flat 2.75% per transaction fee.

Dorsey says Card Case users will eventually be able to use the app to order ahead from their favorite restaurants. For now, all you can do is browse the menu and open a tab when you get within 500 feet of your destination. Meanwhile, with each swipe and tab, Square collects its processing fees, which are adding up: Dorsey recently announced (via Twitter, of course) that Square is processing over $3 million in payments a day. That’s quite the tab.