There are numerous kinds of Anti Tank Guided Missile (ATGM), but they are guided weapons, so don't confuse with Rocket Propelled Grenades (RPGs) that are unguided free flight rockets (like the RPG-7), or projectiles comming from a recoiless gun (like the Swedish Carl Gustav).
However, both ATGM and unguided projectiles use the same principle to achieve a penetration on an armoured target, that is hollow or shaped charge.
There are several families of ATGM:
-"classic" ATGM like the US Tow or the European Milan. They often use a SACLOS (Semi Automatic Command to Line Of Sight) guidance, i.e. the operator must track the target during the time of flight of the missile. It is the laucher and command unit (LCU) that generates guidance commands that are send to the missile by using a despooling wire or a radio link. They usually have a direct trajectory toward their target and low speed inherently to their guidance principle, though they can sometimes be top-attacker (like the TOW 2B) by using a downward directed shaped charge, or supersonic like the russian made AT-6 Spiral.
n order to be tracked by the CLU, the missile has a rear mounted beacon, usually a flare or infrared light. Thus the system can be confused if the target use a form of infrared decoy or jammer. If using a radio data link, the later can be jammed too.
To achieve a kill, the more modern use a tandem shaped charge that can punch through reactive armor, the first warhead detonates it, and the second penetrates the main armor.
They are still in used beacause they are not expensive and remain efficient not only against armoured vehicle but also against foritifications.
-Fire and forget and long range ATGM like the US Javelin, Hellfire, etc etc...
They can use Infrared Imaging ,TV-, laser- or mmW radar-guidance to reach their target. Apart of the laser guided weapon, they are then fire-and-forget weapons. Several flight profil can be selected before launch, and often they tend to use a balistic flight path in order to increase their range and attack their target from above, in its weak point...
For the Hellfire which is a heliborne weapon, variants include laser guidance that can be ensure by the helo or someone else with a laser designator or mmW guided rounds that can be launched in salvo while targeting data are sent before (LOBL) or after (LOAL) launch.
It is recognized that thay have much more potentiel than "classic" ATGMs but they are expensive and often they cannot be controlled after launch so the gunner have to make sure he is firing at the right target.