An example of a late Roman cavalryman, perhaps 5th century AD. His helmet and chainmail already look very much like the armour of later medieval knights. He bears a light, round shield and a lance for stabbing. The sword of the Roman cavalryman was the spatha, a long-bladed weapon, granting the rider a much greater reach than the legionary's short gladius.
Much of the precise armoury and weaponry of late Roman cavalry is guesswork. In this case, spot the quiver carried behind the saddle, holding arrows for use with the bow.
The prefered mode of battle for the Roman cavalry (ala) was fall into the rear or the flanks of an enemy already deployed against Roman infantry. It proved at its most devastating when it rode down fleeing troops, lancing the fleeing soldiers in their backs. In fact most of the slaughter in ancient battles is thought to have occured, when the opposing army broke and fell into disorder and the cavalry fell upon the panicked and fleeing enemy.
Note that the Roman cavalry rode without stirrups.