In a wider sense, Kickboxing arts include all stand-up combat sports which allow full-contact punching and kicking, although within this category there are styles that denominate themselves as 'Kickboxing'.
Some of those best well-known styles include Muay Thai, American Kickboxing and Savate. Other styles that may fit in that category are Sanda (a Kung Fu style), Taekwondo and some Karate styles.
Muay Thai can be considered as the most complete stand-up fighting style because it allows all kind of strikes (including the use of elbows and knees) both above and below the waist. Because it contains a much wider range of techniques, Muay Thai is usually distinguished from other KickBoxing styles.
The term 'Kickboxing' was introduced in the 1960s in Japan to describe a hybrid martial art combining Muay Thai and Karate created in 1958.
Most of those various styles have currently assimilated the Boxing techniques.
In the United States, the first martial art in this modality was named "Full Contact Karate". It represented a Karate style created in the 1960s that allowed punches to the face and kicks to the legs, something which is vetted in nearly all Karate styles. Boxing techniques would then be added, and this fighting style would be later named 'Kickboxing'. Most of the punches come currently from Boxing.
Muay Thai came from Thailand and is at least a thousand years old. It is derivated from an older combat art named Muay Boran that was developed for a warrior to use if he lost his weapons in battle. It became later popular as a form of entertainment for temple festivals and local celebrations.
From 1921, Muay Thai matches began to be disputed in rings with protective gloves, referees and timed rounds.
Savate (or French Boxing) is a French martial art which uses only the hands and feet as combat weapons. It was developed from street fighting in Marseille, France. 'Savate' is a French word meaning "old shoe" and the name is related to the fact that it is the only fighting style in which its practitioners use a specific shoe.
Michel Casseux (1794–1869) and Charles Lecour (1808–1894) were responsible for shifting Savate from street-fighting to a modern sport.