A weapon used to "kill" armoured fighting vehicles - whether by destroying them outright (a "K" kill), immobilising them so that they are forced to drop out of the battle (an "M" kill … can also apply to a vehicle which has been incapacitated by damage to weapons or sensors) or by incapacitiating the crew (A "P" kill, sometimes called a "soft" kill). Other classifications of kill may exist depending how much detail your service likes to bother with.
These weapons are roughly as old as the armoured vehicles they are designed to deal with and so date from about the start of the 20th Century when rudimentary thought was put into combatting armoured cars and armoured trains, but they were really spurred into growth by the development of the tank during WW1.
The first solutions tried to the enemy armour were generally either heavy weapons such as machine guns (to which many early AFV were far from immune) and high powered rifles (the ancestors of the modern anti material rifle) or artillery cannons, temporarily re-tasked to fire at the enemy over open sights, sometimes using kinetic armour piercing rounds developed from naval designs. Where these were lacking, the infantry did what they could with grenades, mines and similar improvised weapons.
From the end of the Great War the anti tank weapon continued to evolve - specialised anti tank guns were developed from the original artillery pieces, the anti tank rifle evolved further (to no great effect) and a few specialised anti tank grenades - usually large and dangerous to use - were developed.
And then WW2 arrived, arguably the golden age of tank warfare and therefore a breeding ground for anti tank weapons. Just before the outbreak the moltov cocktail had officially been developed (although some accounts show similar weapons in use at least as early as the Polish-Bolshevik war of the 1920s), and this - either in its improvised or commercially made forms would remain popular. But far greater things were afoot - the Munroe effect was applied to weapons development to create the first Shaped Charge rounds (e.g. HEAT), taper bore and discarding sabot designs were used to enhance the effect of kinetic armour piercing rounds and recoiless designs made weapons smaller and lighter, allowing them to be dispersed more widely. Anti-tank grenades remained in use - often become heavier and harder to use to progressively less and less effect. By the end of the war rockets were a common solution to a tank and the Germans had sucessfully developed the first LAW in the shape of the Panzerfaust.
Since WW2 the gun-versus-armour race has continued, tanks become better armoured and weapons try to outdo them: the anti tank gun became essentially obsolete and the rocket evolved into the anti tank guided missile. More and more sophisticated types of ammunition have been developed since to strike at tank armour from unusual directions and further systems such as directed energy weapons and railguns remain in development. The efficacy of modern anti tank weapons can make them grossly overpowered against lesser AFVs - to the extent that a modern APDS round can go in one side and out the other of some light armour (such as armoured personnel carriers), leaving the vehicle - if not the people inside - still functional. In the same vein, unless used against a main battle tank a modern anti tank missile may be more expensive than its target.
Artillery tends to remain useful due to its ability to apply overwhelming force, often at (relatively) low cost.
The growth of airborne anti tank weaponry (most notably as deployed on the attack helicopter) has lead some authorities (although not yet a majority, or even nearly so) to wonder if the tank still has a role to play. However, not all enemies can afford to deploy attack helicopters so this remains a moot point for the foreseable future.
Attacking the crew for your "P" kill remains an option - the simplest method being to attack with grenades and/or small arms when they are exposed. Other techniques involve using specialised ammunition (such as HESH rounds) to flake pieces of spall off the inside of the armour - although modern, non-homgenous plate makes this increasingly hard. "Softer" techniques (apart from psychological warfare) tend to fall foul of the Hague Conventions or the Geneva Accords, being either prone to causing malicious injury (like blinding lasers) or comprising chemical, biological or radiological agents (ironically this would include chemical less-lethal weapons such as sedative gases).