The first thing you have to realize is that this is how animals die in the wild. When wolves in the same pack fight for dominance they try to "hamstring" each other, literally taking a chunk out of the tendons you can feel on either side of the back of your knee as you're sitting down. The winter my father first took me ice fishing I found a trail of red which let to scattered clumps of what looked like dried up shoe laces. He explained to me that it was the way smaller coyotes would take down a deer; after chasing it onto the ice they would bite at the tendons running down the back of their legs, rendering their escape helpless.
So, you see, fully rupturing one of these all important tendons in the leg is a bad idea.
The Achilles tendon, or Tendo Achilles as it is sometimes referred to as, is the tendon which connects the calf muscle to the heel of your foot. To be most technical (aspiring med school students should pay attention here) the tendon runs between the gastrocnemius and the calcaneus. The tendon lies just beneath the skin and can be followed up the leg for about four inches before the calf muscle takes prominence. Controlling both lateral and orbital foot movement, the Achilles tendon is arguably the second most important movement related tendon ranked beneath only the ACL.
The two most common, and painful injuries sustained by the Achilles Tendon are Achilles tendonitis and complete rupture of the Tendo Achilles. The first is characterized by a localized reddening of the area as well as a sharp pain accompanying activity which gradually fades as the tendon warms up. Tendonitis is generally caused by the friction or inflamation of the tendon due to forces inside the leg where the tendon is attached. Rupture of the Achilles, as I have found, is generally characterized by the victim falling down. An audible snap is generally heard, and the foot no longer may be pointed either towards nor away from the patient's knee under their own volition. Ruptures are often mistaken for simple sprains due to the immediate swelling which only appears to be controlled by application of ice. DO NOT MAKE THIS ASSUMPTION. Always seek immediate medical assistance for injuries to the major joints or ligaments of your body (ankles, knees, elbows, wrists, shoulders, and neck). A rupture can be further verified by running one's fingers over the back of their leg, starting at the heel and working up towards the knee. In the event of a rupture, a dell can be found, where the tendon seems to disappear completely. This is the worst case scenario.
The treatment of a case of tendonitis is simple. Stop doing the activity that caused the inflamation for three weeks. If you are an athlete, I will allow you to stop laughing before I continue.
Done laughing yet? Great. Just like abstinence is the only perfect method of birth control ("Oh Mary, it had better be immaculate. It had better be!") a period of complete rest is the only perfect method of making tendonitis inflamation relax and subside. Most often, tendonitis pain and inflammation will subside by reducing activity by 25% and taking a pain reliever such as Tylenol or Advil. If you are a runner running 21 miles per week, you should probably cut down to no more than 15 miles per week. For a more accomplished runner clocking 60 mile weeks, three weeks at 40 miles per week would be advisable. Another important "treatment" of tendonitis is constant icing. The two methods I like to use are direct application or ice massage. Direct application would include crushing some ice cubes in a plastic bag, and then applying the bag to the area that is sore, using a tee-shirt or a cloth as insulation to prevent freezer-burn to your skin. Ice massage, which feels incredible, involves filling several paper cups with water and freezing them. By peeling back rings of the paper you have both a block of ice to massage your inflamed region with and a way to hold it with the remains of the cup. These are by no means medical treatments, but simply things which have worked for me. YMMV
A ruptured Achilles has no such conventional methods of healing. While it is theoretically possible for a partial rupture to heal itself after several months of relative innactivity and no weight bearing, full function will never be retained. Thankfully, modern surgery has created solutions to a torn Achilles. Former practices involved creating an incision on the back of the leg, pulling the bits of tendon back together, and sewing up the remains. This method was largely inneffective. Reason number one: the tendon was now too tight, no longer in physiological tension. This made the foot of the patient point downwards, at angles up to and sometimes exceeding 30 degrees. This problem can take a lifetime of physical therapy to solve. The newer method of patching up a ruptured Achilles is a bit more invasive, but much more efficient. This method involves a 8"-10" incision along the calf and the harvesting of a small rectangle of fibers from the medial gastrocnemius to bridge the gap of the ruptured tendon. Both torn ends are sewn into this new tendon, which is remarkably of the same material, and will not be rejected by your body. The entire site is then sewn back up and put in a hard cast for 6 weeks after which a soft cast is used and crutches are slowly weaned away. Physical therapy then ensues and close to full strength will return after approximately one year of slow and steady progress. Rushing the recovery will surely set you back several months. Rushing return from an injury such as this is a very bad thing. After recovery the Achilles tendon, while not being as strong as before the injury, will often be strong enough to be fully functional in the areas of running, jumping, and being otherwise active.