Just before WWII an American Officer put a "Hollow Charge" round at the end of a Rocket, and than put the Rocket inside a steel Tube. The Steel Tube was to contained the rocket while it used up its fuel. Thus was invented the WWII Era Bazooka. The Hollow Charge effect had been know since the late 1800s but how to use such a weapon? A Hollow Charge Grenade was proposed, but how do you get the Grenade to the target? The Bazooka solved that problem by attaching the Hollow Charge Round at the front of the Bazooka's Rocket. The Bazooka worked by one man aiming the weapon and the loading the weapon from the rear. The Rocket completely used up its fuel before it even left the launching tube. Thus the Bazooka was a long metal tube, but was effective enough that the Germans copied it soon after running across it in the hands of the Russians in 1941.
As to the Hollow Charge Grenades themselves the Russians seems to have used some during WWII but found out the same problem the US had with the Grenades, how do you get the round to the target? To better understand the problem lets me explain what a "Hollow Charge" Round is (HEAT, or High Explosive Anti- Tank, is just the Military Jargon for a Hollow Charge Round).
A "Hollow Charge" is a explosive shell that penetrates armor through the chemical interaction with the armor instead of sheer power. How the Hollow Charge works is first it hits Armor Plate than an Explosion occurs NOT at the tip of the shell but at its base. This explosive charge becomes a hot stream of liquid that is than channeled by the rest of the shell to the armor. It than "melts" through the Armor destroying the tank.
Thus a Hollow Charge round's main advantages over other anti-armor weapons is that to penetrate armor the Hollow Charge is NOT dependent on the speed of the shell. For the weapon to work all you need to do is get it next to the armor.
A Hollow Charge (i.e HEAT Round) disadvantages are several, first the round itself is NOT aero-dynamic i.e. it has a big hollow point in its center (This is generally covered with a thin sheet of metal or Plastic to give the round some aero- dynamic shape. The Plastic or Metal sheet springs away from the round when it hits the tank.). Second it works best with no spin and low speed (thus spin to make a weapon accurate hurts the Hollow Charge effectiveness. Thus Hollow Charge weapons are almost always low speed projectiles). This low speed also restricts distance the weapon can be used for if used against a moving target, the further the target is away the longer time the round will have to travel and the greater chance the target will go somewhere other than with the shooter of the HEAT round thought the target would go.
Thus Hollow Charge (HEAT ROUNDS) have generally been used in low speed close up weapons (With Long Range Anti-Tank Missiles being the big exceptions. In such weapons accuracy can be guided so spin can be minimized, and if the target moves, so can the aiming point of the missile).
In the 1950s the Russians came up with their own solution to the problem of getting the HEAT Round to the target, it was the Rocket Propelled Grenade (RPG) - 1. Quickly replaced by the RPG-2 and than the RPG-7 of Vietnam War Fame. Unlike the WWII era Bazooka, the RPG is loaded from the front by the gunner, who than aims the round at a target. He shoots and a rocket motor kicks in launching the round in the direction of the target. Once beyond the immediate area of the gunner a Second Rocket Motor kicks in and carries the round to its target. This two stage rocket system permits a much smaller launcher to be used compared to the Bazooka (The RPG is a one man weapon, not the two man weapon the Bazooka was). Since the RPG-2 was used in Vietnam various improved versions have come out (RPG-29 are the last version I heard of).
The point I am making here is the "Grenades" being used are NOT Grenades that can be thrown but fairly sophisticated pieces of equipment that can be used at some distance from the target (Generally less than 300 yards). The operator has to be protected by other troops (for the use of the RPG generally precludes the use of a Rifle). Thus a RPG attack, even if the only thing fired is a RPG, is generally more than a lone attacker.
I mention this is that the heading for your listing implies this was just a mere Grenade attack, where someone threw a Grenade he had in his pocket. The RPG is a Rifle size weapon, not easy to hide on someone's body. Like the Mortars being used in Iraq, getting either of the them to the target without being discovered by the US Troops implies that someone other than the US Army controls the Streets of Bagdad.
For more information on RPG and other "Threat" Weapons see
http://fas.org/man/dod-101/sys/land/row/weg.pdf