The aptly-named Companion Cavalry served under Alexander the Great's Macedonian banner and were based on King Philips learning of Theban Epaminondas (of which Alexander himself was trained as such). Companion Cavalry were chosen from the ranks of Macedonian nobility and were often times individuals who served the king well in previous battles. The component consisted of a rider, his steed and a thrusting spear.
On the battlefield, the objective of this particular equine unit was to act as shock elements. While the powerful Macedonian phalanx approached and made contact with the enemy, the Companion Cavalry was held in reserve until the right time to strike. As the phalanx broke through the enemy formation lines, the cavalry was unleashed onto the broken lines - usually along the softer-protected flanks - to further chaos and force the lines backwards. In this strategy, the enemy was forced to either fight to the death or turn and run which opened them up to further confusion and attacks.
The Companion Cavalry rider was a lightly-armored soldier protected by helmet and cuirass. Beyond that he was designed to be nimble as were the new formations of Greek phalanx as fielded by Alexander. The steed was of a powerful breed and light protected as well. Armament for the rider consisted of his standard slicing sword for close-in work and a shortened form of the phalanx soldier's sarissa - a thrusting spear of proper length (infantry sarissa's could reach an astounding length of 18 feet!).
Companion Cavalry operated on Alexander's own personal orders and were usually held in reserve until the "proper moment" was unveiled. This system proved quite effective in the dismantling of the Persian Empire - most notably at the Battle of Gaugamela (Alexander's 47,000 versus the Persian 86,000) - where the future of the known world was decided in favor of Alexander and his Companion Cavalry - a loss that the Persian Empire and King Darius would never fully recover from.