You buy your first product with a new brand and get a welcome email. In the email, there's a voucher for a second purchase, which you add to your mobile wallet app. A week before its expiration date, you get a push notification to remind you about the open offer.
A new customer comes into your store and simply taps her phone at the cash register to upload a digital loyalty card to her mobile wallet. Whenever that customer comes near your point of sales, she receives the most relevant promotions currently running through push.