Cavalry tactics
The first regular cavalry unit to mechanize was the 11th Hussars of the British Army, switching from horses to armored cars in 1928. Since then, many cavalry units have mechanized and switched to armored vehicles and armed helicopters, with horses only being used for ceremonial purposes, if not phased out of service entirely. However, some modern units, such as the Indian Army's 61st Cavalry and some People's Liberation Army's border units in Xinjiang and Inner Mongolia, continue to use horses on deployments.
Examples of modern military vehicles built specifically for the cavalry role include the M3 Bradley CFV and the M113 ACAV.

Air cavalry: Air cavalry, originally sky cavalry is a United States Army term that refers to helicopter-equipped units that perform reconnaissance, screening, security, and economy-of-force missions. The term and unit designation properly only refers to those squadrons (i.e., battalion-level organizations), and some independent troops (i.e., companies), affiliated with historical U.S. cavalry regiments, that perform the traditional cavalry mission. After the Vietnam War, there also existed one independent brigade-sized air cavalry organization, the 6th Air Cavalry Combat Brigade.
U.S. air cavalry squadrons consisted of three air cavalry troops, one armored cavalry troop, and a headquarters and headquarters troop. The air cavalry troops consisted of an aero-scout platoon, an aero-weapons platoon, an aero-rifle platoon, a service platoon, and a headquarters and operations platoon. The troop was commanded by a major, with a captain as executive officer, and a troop first sergeant. Each platoon was commanded by a captain with a lieutenant as assistant platoon commander/section leader and a sergeant first class as platoon sergeant.

References: Verbruggen, J.F. (1997). The Art of Warfare in Western Europe during the Middle Ages. The Boydel Press. ISBN 0-85115-570-7.
Polybius World History
German Wikipedia, partly translated article
Cavalry Tactics during the Napoleonic Wars

External links: American Civil War: US cavalry tactics ("Cooke's Cavalry Tactics (1862)")