Someone who specializes in straightening teeth is an expert in orthodontics. If you have braces, you know a lot about orthodontics, from brackets and rubber bands to the nasty retainers you're forced to wear after the braces have been shed.
Dentists who focus on correcting crooked teeth are in the field of orthodontics. Sometimes orthodontics are as straightforward as a year of metal braces, but in other cases a patient might require surgery to correct the problems with their teeth and jaw. These procedures, as well as retainers and braces, are known as orthodonture, and the expert in charge is an orthodontist. The Greek roots of all these words are orthos, "straight," and odont, "tooth."