Many people have and use microwave ovens to cook. Officially microwaves do no emit harmful radiation, like that of an X-ray, but they still emit some. They have also been proven to interfere with older pacemakers. I've always wondered how microwaves affect the food while it is cooking.
Using plastic containers in a microwave is not a good idea in my opinion. The plastics from used containers, like yogurt or margarine, will leach into food. I'm not an expert but I think heat added to anything usually changes it's properties and chemical composition.
Some studies have suggested that using the microwave to heat or cook a variety of foods reduces the nutritional benefits of some foods. It has been found to reduce flavonoids in broccoli, B12 vitamins in other foods and infection fighting qualities of frozen breast milk. Other studies have found that microwave cooking has no impact on health benefits of foods.
I'm not sure about the impact of microwaves. I have modified how I use it and how much I use it and if it wasn't there I don't think I would miss it. Just like anything else, studies will come out for and against. Everyone has to make their own judgment call.