How does a Sharia-compliant Islamic credit card work?

It does not work on interest charged on the outstanding balance when repayment is late.

The Islamic bank relies on one of two formulas: either charging fixed monthly/annual administrative fees in return for making the credit limit available, regardless of the amount used, or buying under the "Tawarruq or mini-Murabaha" formula (Tawarruq: a commodity purchase resold for cash) for each settlement transaction, and the card is completely blocked from being used at merchants that are not Sharia-compliant (such as liquor shops or betting outlets).