It depends on what they are. Most grayish/blackish stains will come out. Unfortunately, anything with a dye will pose a problem. There is no way to remove a dye spot from your carpet without affecting the original dye applied when the rug was manufactured. So, wood stain, food coloring from popsicles, hair dye, some markers, dyes in some candle wax, etc, often can’t be removed. There are a few people that specialize in spot dying carpets. This is a process where the spot is bleached out and a new dye is applied to match the existing color of the carpet. But, it’s very tricky and raises special new problems. An exact color match is never guaranteed, some dyes can’t even be bleached out, and the bleaching effort can affect the PH balance and leave an orange ring.