In principle, paying for something should be easy. Everybody—the buyer and the seller—wants the transaction to go through. But as I noted in my Scientific American column this month, America's effort to streamline—and secure—payments by letting us pay for things with our cell phones keeps getting mired in squabbling across industries: the phone makers, the banks, the cell phone carriers and the retailers. Everyone wants to control the way we pay.

It's fun, though, to watch how the forces of commerce keep trickling ahead, like water around a rock in the stream. Here are some of the most interesting ways to pay for things with your phone—that don't involve Apple or Google.

Square: This tiny, free, white, one-inch credit-card reader plugs into your phone's headphone jack—and lets you, the mere nobody, accept credit cards. You don't have to be a store. You can be a piano teacher, babysitter, lawn-mowing teenager or elementary-schooler at a lemonade stand—and accept credit cards! The reader is free; Square takes 2.75 percent of each transaction.

PayPal Here: These guys came up with their own competitor to the Square Reader. Once again, it snaps into your headphone jack. The app is more complicated, but offers even more features: You can use the phone's camera to accept a check by taking a picture of both sides, for example.

Square Cash: You can't believe this works, but it does: You can send money to anyone with an email. You get Square's phone app and tell it your debit-card number. You address an email to your friend, with "cash@square.com" in the CC line and a dollar amount in the Subject line. That's it: The money is transferred instantly to her bank account. (The first time she accepts, she must enter her debit-card number.) There's no fee, no charge, no name and password, nothing to sign up for.

LoopPay: Here's a way to pay by phone—that's instantly compatible with hundreds of millions of merchants' existing credit-card readers. You input all of your cards to the phone app and plug a little, white, square, plastic fob into your phone's headphone jack. It sends out a magnetic signal that tricks the credit-card reader into thinking that you've actually swiped that card through it. You just hold the Loop near the card-reader slot and—beep!—you've just paid. Also available built into a phone case.

Venmo: This service lets you quickly and easily send money to or from anyone else on Venmo's system. You don't have to own a smartphone; you can even send money by text message. And it's free for consumer use. 

Which one of these will take over? As usual in technology, there probably won't be one winner; we'll wind up with a web of overlapping rivals. But it's clear that paying by credit card at a big store is no longer the only way to do business.