Spider veins, which are also known as telangiectasia, are small superficial thread-like veins nearer to the skin surface. They most often occur on the back and sides of the thigh and just below the knee.  Spider veins can appear on any part of the body, including hands and face, but they most commonly appear in the legs from increased pressure and decreased blood flow. If you have noticed tiny, colorful, red veins on your legs, they are probably spider veins or telangiectasia. USA Vein Clinics, the nation’s largest network of vein clinics.