Spider veins, or broken blood vessels on the thighs and calves, are a symptom of abnormalities occurring in the circulatory system and are sometimes a harbinger of future varicose veins. These are tiny tangles of permanently dilated vessels that look like blue or red threads on the skin. This is a condition that needs to be treated as it leads to serious complications. Bursting blood vessels on the legs can be treated with laser therapy, sclerotherapy and pharmacotherapy.