We have many ways to replace missing teeth. They can be classified into two basic categories: fixed appliances (something that stays in the mouth) or removable appliances.
Teeth can be lost or missing for many reasons. Some people never develop a full set of teeth. Early detection of this in a young patient can sometimes be solved orthodontically by moving other teeth into the missing tooth's place. Sometimes teeth are too badly infected (decayed) that not enough tooth structure is left to restore predictably. Other times the infection is too deeply seeded in the supporting tissues of the tooth (either due to a carious lesion or periodontal disease) that the whole tooth becomes loose and unable to be retained. In these cases, extraction is needed as a treatment of the infection. Other times, teeth are lost due to injury. The tooth could be fractured in a way that is not restorable. Sometimes the tooth can be knocked out completely (avulsed). With proper immediate care of the avulsed tooth, it can sometimes be re-implanted into the socket and saved.