In order to avoid costly penalties, everyone needs to remember to file for Medicare during the seven (7) month window around their 65th birthday.  Filing for Social Security can occur at the same time, but need not.  Remember, every year you delay taking Social Security increases your benefit by about 8% a year.  So, although you need to file for Medicare around your 65th birthday, you can delay filing for Social Security until your 70th birthday to receive your maximum allowed benefit.