Your third molars are more commonly called 'wisdom teeth.' Usually appearing in the late teens or early twenties, third molars often lack the proper space in the jaw to erupt fully or even at all. This common condition is called impaction. When any wisdom tooth lacks the space to come through or simply develops in the wrong place of your jaw and becomes impacted, problems can arise. Primarily, damage to adjacent teeth and crowding occurs. In certain cases, the wisdom teeth that cannot come through becomes inflamed under the gums and in the jawbone, causing a sac to develop around the root of the tooth that then fills with liquid. This can cause a cyst or an abscess if it becomes infected. If either of these situations goes untreated, serious damage to the underlying bone and surrounding teeth and tissues can result.
Teeth that have broken to the gumline or have high amounts of decay causing pain sometimes cannot be restored.
There are many reasons to restore a tooth versus pulling the tooth and they are all very person and case specific. Here is a small list of reasons for extraction: