Compression fracture of vertebra would heal on its own but can have long standing complaints of pain and deformity even after the fracture has healed. If the fracture is acute (few weeks) then a vertebroplasty is beneficial (its a procedure done under anaesthesia, where cement is injected into the vertebra after restoration of the vertebral height using balloon) for chronic (old) fractures, if you have pain - you can try physical therapy or brace. Role of surgery is very minimal if you have neurologic symptoms of tingling, numbness or weakness due to the fracture.