With a credit card, you can carry a balance and accrue interest if necessary. Note this is not advised by me. The points game does not work well, if you are carrying a balance and accruing interest. See #4 in Let’s Get Started To Earning Free Travel.
Pay no foreign transaction fees when you use your card on purchases made outside the United States.
Basically, you use your card to book travel. You then redeem your miles online or by phone to get reimbursed for your purchase. After that, your account will be credited for the purchase, and you will see that credit on your statement. Learn more about redeeming miles here.