Capillaries are the smallest blood vessels in the body that connect arteries to veins. When capillaries narrow or widen too quickly, their walls can tear causing blood to seep out. This gives the appearance of thin red or purple lines under the surface of the skin. While these lines are usually not painful, they can be displeasing in appearance.
Broken capillaries form in areas where the skin is thin or sensitive, such as the face. Common causes of broken capillaries include exposure to hot weather, strong winds blowing on the face, sunburn, pressure or trauma to the face. Dehydrated, dry and sensitive skins often have thin skin that provides less protection and therefore, these skin types are the most commonly effected by broken capillaries.
There are a number of different procedures available for the effective treatment of broken capillaries. These include:
Electrolysis:
Electrolysis treatment involves the use of a fine needle by a dermatologist to send an electrical current into the skin destroying the capillaries. Although this is a very effective treatment, it may cause small scars where the needle is inserted.
Surface Laser Treatment:
This technique involves sending very strong bursts of light through the skin onto the vein. This makes the vein slowly fade and disappear. No needles or incisions are used, but the heat from the laser can be quite painful.
Sclerotherapy:
Sclerotherapy involves the insertion of a small needle into the skin and the injection of a liquid chemical into the vein. This causes the walls to swell, stick together, and seal shut. This stops the flow of blood, and the vein turns into scar tissue. In a few weeks, the vein should fade.
Micro needling:
Micro needling involves passing a small roller covered in very fine needles across the skin a number of times in different directions. This causes the capillaries to break up, making it easier for the body to absorb them. 
