Armoured warfare
Airborne threats: Tanks and other armoured vehicles are vulnerable to attack from the air for several reasons. One is that they are easily detectable—the metal they are made of shows up well on radar, and is especially obvious if they are moving in formation. A moving tank also produces a lot of heat, noise and dust. The heat makes seeing them on a forward-looking infra-red system easy and the dust is a good visual cue during the day.
The other major reason is that most armoured vehicles have thinner armour on the roof of the turret and on the engine deck, so an anti-tank guided missile or bomb (from an attack helicopter, unmanned combat aerial vehicle, ground-attack jet or small drone) hitting them from the top can be deadly even if it has a small warhead. Even a small automatic cannon is powerful enough to penetrate the rear and top sections of the engine compartment of a tank. Loitering munition (suicide drone) is also used to attack tanks in modern warfare.

Certain aircraft have been developed to attack armoured vehicles. Most notable is the purpose-built Fairchild-Republic A-10 Thunderbolt II, also known as the "Warthog". Although able to carry a number of different missiles and bombs (including anti-tank ordnance such as the AGM-65 Maverick), the A-10's main weapon is a 30 mm GAU-8/A Avenger Gatling gun which is capable of firing 3,900 depleted uranium armour-piercing rounds per minute. The Russian equivalent is the SU-25.

Similarly, a number of helicopter gunships have been designed mainly to engage enemy armoured vehicles. The AH-1Z Viper, AH-64 Apache, HAL Light Combat Helicopter, Denel Rooivalk, Eurocopter Tiger, Ka-50 Black Shark, Mi-28 Havoc, A129 Mangusta and Westland Lynx are examples. Helicopters are very effective against armoured vehicles for many reasons. The AH-64D Longbow Apache, for example, is equipped with an improved sensor suite and weapon systems and the AN/APG-78 Longbow Fire Control Radar dome installed over the main rotor.
Airborne threats can be countered in several ways. One is air supremacy. This is what the United States relies on most, which is demonstrated by their distinct lack of effective short-range, mobile air defence vehicles to accompany armoured units. Most other countries accompany their armoured forces with highly mobile self-propelled anti-aircraft guns such as the German Gepard or the Soviet 9K22 Tunguska, short and medium-range surface-to-air missile systems such as the SA-6, SA-8 and SA-11, or combine both on the same vehicle (the Tunguska for example can also host SA-19 SAM missiles). The usage of anti-aircraft rounds fired from the main gun of a tank has been increasing over the years. An example is the HE-FRAG round from the T-90 which can be detonated at a set distance as determined by its laser range finder.

Engineering support: Armoured warfare is mechanically and logistically intensive and requires extensive support mechanisms. Armoured fighting vehicles require armoured vehicles capable of working in the same terrain to support them. These are operated by the appropriate branches of the army, e.g. recovery and maintenance vehicles by the REME and combat engineering vehicles by the RE in the British Army. These include:

Armoured recovery vehicles (ARV)—many of these are based on the chassis for the vehicle they support. E.g. the ARV for the UK Challenger tank is a Challenger hull onto which a winch is added.
Armoured supply vehicles
Combat engineering vehicles (CEV), e.g. bulldozers
For transporting tracked AFVs over highways, heavy transporters are used, since AFVs are prone to malfunction and their tracks also ruin the highways.

Light tanks and tank destroyers: While tanks are integral to armoured warfare, when power projection is required, the inability to perform rapid deployment has always been a limit of heavy main battle tanks.
It takes a few weeks to transfer tanks and their supporting equipment by air or sea. Some tanks and armoured vehicles can be dropped by parachute, or carried by cargo airplanes or helicopters. The largest transports can only carry one or two main battle tanks. Smaller transports can only carry or air drop light tanks and APCs such as the M113.
The desire to create air-portable armoured vehicles that can still take on conventional MBTs has usually resulted in ATGM-armed light vehicles or in self-propelled gun style vehicles. The lack of armour protection is offset by the provision of a first-look/first-hit/first-kill capability through the mating of a powerful gun to superior targeting electronics, a concept similar to that of the US tank destroyers of World War II.

Vehicles which have put such considerations into practice include the Stingray light tank, AMX 10 RC and B1 Centauro. Most such US projects to create such vehicles have been abortive, e.g. the M8 Armored Gun System. The most common was the flawed M551 Sheridan light tank. This was an air-portable tank capable of destroying heavier tanks using the revolutionary (for the time) 152 mm CLGP launcher. The combat effectiveness of this tank was limited by the unreliable MGM-51 missile. The latest iteration of the mobile anti-tank gun platform in American service is the M1134 anti-tank guided missile vehicle, a Stryker variant equipped with TOW missiles; most modern militaries operate comparable vehicles.
Though limited conflicts (such as the insurgency in Iraq) rarely involve direct combat between armoured vehicles, the need to defend against insurgent attacks and IEDs has resulted in the application of armour to light vehicles and the continued use of armoured transports, fighting vehicles and tanks.

See also: 

Theorists and practitioners: 

Notes: 

References: 

External links: Tanks Encyclopedia
Japanese Tanks and Tank Tactics Chapter II: Tactics
Historic films showing tank warfare during the First World War at europeanfilmgateway.eu
Educational video of how armored vehicles are used on the battlefield.