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Currently Continental Airlines operates under United Airlines. This airline has its own credit card called MileagePlus Explorer card and it is issued by Chase. You can consider applying for this card. However, if you are not going to fly with United, we would recommend you to apply for a regular credit card with miles rewards. Such card will allow you easily switch airlines and redeem miles with literary any airline. Also, if for some reason you do not travel, you can use miles rewards credit card to earn miles on your everyday purchases. The miles rewards per dollar spent are fixed for all shopping categories.