Why does mildew appear on your clothes after you wash them?

Idk if it's my washing machine, or i'm doing something wrong but When I wash mostly my kids clothes they come out of the washer with black spots everywhere like mildew spots. what the heck is causing that and how can I avoid it? I mean it happens on brand new items that I wash for the first time I don't get it, but I can't keep throwing things away I don't have that kinda cash to waste.