Card tokenization
Replacing the card number with a surrogate that only works in one specific context, so that stealing it gets you nothing.
There are two kinds. Payment gateways such as Stripe have long kept the card number in their own vault and handed the merchant a reference instead. That shrinks the merchant's PCI DSS burden dramatically, since it never sees the real number. Network tokens, defined in EMVCo's 2014 specification, go further: the card network issues its own 16-digit number locked to one device or one merchant, and each purchase is signed with a one-time cryptogram.
Apple Pay, launched in October 2014, was the first big breakthrough. The card number in your phone is not the one embossed on your card. A pleasant side effect is that network tokens update automatically when the bank reissues a card, so subscriptions no longer break just because a card has expired.