Most types of plastics are safe to put in a microwave oven. In fact, since microwave ovens are so common, the majority of plastic plates, bowls and cups are made specifically for that purpose.
Not all plastics should be used in the microwave oven, however. Plastic dishes used for heating up food should be food-safe, as outlined by the United States Food and Drug Administration. Most microwave-safe plastic dishes include a statement on the packaging that they are safe for use in a microwave or dishwasher. Many are constructed so they can go straight from the freezer to the microwave.