As co-owner of Billykirk, a leather goods brand based in Jersey City, N.J., Chris Bray has devoted the past 20 years to hand-crafting wallets, among other accessories. He can wax philosophical about how “your oils, your skin, your travels” affect the wallet that you carry around. But when Mr. Bray goes out at night, he takes just his ID, one credit card and a few business cards, tucked into a slim card case.

“Simplify your life,” he said. “Nine out of ten times, if you have a bi-fold wallet, you’ve got crap in there you don’t need. You’ve got a ticket stub from three years ago.”

This from a man who sells bi-fold wallets in four colors. But in recent years, the physical wallet’s central role in our lives has been greatly reduced, as have the size of wallets themselves. As tech companies have introduced mobile apps like Apple Pay and Google Pay in an effort to make the smartphone into a digital wallet, “real” ones — long a fallback of the holiday gift season — are shrinking, or disappearing altogether. Some are becoming gizmos themselves, as if to seem more current: popping out cards with the press of a button and offering benefits like locating services or radio-frequency identification (RFID) blocking, intended to protect against credit-card or identity theft.

For men, the classic multi-pocketed model is losing popularity to card cases like the one Mr. Bray carries. They aren’t much bigger than a credit card, and slip easily into a front pocket.