The process of pasteurisation gets rid of harmful bacteria in milk, but bacteria can still grow, especially if the milk is kept out the fridge for too long. However, research suggests that unopened milk, stored correctly, can still be good up to a week after the listed date, while opened milk should be fine for two to three days past that date. If it starts to look, smell or taste sour, or has a strange appearance, that's when to stop drinking it. A sip or two of sour milk, while pretty unappetising, is unlikely to make you ill.