All equestrian activities requires knowledge and practice of horse care and partnership. In some cases the rider has to ride hands-free to partake in the activity, such as mounted archery. It takes great skill and courage to practice these activities.
Jousting Two horse-mounted participants charge at one another, a pole in one hand, prepared to knock the other off their mount.
Mounted combat is striking at your opponent with a sword (padded) while both people are riding. There are versions of this where you try to knock a crest off your opponent’s helm.
Mounted archery is bow and arrow shooting at targets from horseback whilst in motion.