These soldiers were often auxiliaries and typically played a supporting role for the Roman infantry. In early Republican Rome the upper class provided the cavalry as they were the only ones able to afford the more expensive equipment and maintenance of a horse. However, as time progressed and the state began to supply its soldiers with equipment, joining the cavalry became less and less popular and eventually Roman cavalry was supplied mostly by other nations and mercenaries. However, Roman armies were focused on infantry and cavalry were far less important to them than other contemporary armies.
Despite the lack of focus on Cavalry, Rome still did utilize some fairly complex tactics, including the wedge formation as shown. Cavalry played many supporting roles such as a quick response force to enemy raids, a flanking force, finding supplies for the army and raiding the enemy. The Eastern Empire eventually even adopted cavalry archer tactics to counter those of its enemies but for most of its history, Roman cavalry fought primarily with a spear or sword.