At the moment only 1 style of Taekwondo is part of the Summer Olympic Games: Kukki-won Taekwondo (which is also known as WTF Taekwondo or WT Taekwondo).
Kukki-won Taekwondo is one of the two most popular styles of Taekwondo in the world. It’s also known as WTF Taekwondo (‘WTF’ stands for ‘World Taekwondo Federation’ – although recently the World Taekwondo Federation changed their name to just World Taekwondo, or WT, so the style is also now known as WT Taekwondo).
Sparring in Kukki-won Taekwondo heavily favours kicking techniques, which has led to the popular misconception that hand techniques are not part of Kukki-won Taekwondo – they are, they’re just not used often in sparring.
The other of the two most popular styles of Taekwondo in the world is Changheon-yu Taekwondo. Sparring in Changheon-yu Taekwondo sees a more even use of hand and foot techniques. Practitioners of Changheon-yu Taekwondo have long wanted the style to be part of the Olympic Games. Since it isn’t, any Changheon-yu Taekwondo practitioner who has wanted to compete has had to switch to Kukki-won Taekwondo.