Close–there are a variety of KATUSHA-TYPE ROCKET LAUNCHERS, including very small man-portable ones, that carry out a similar role as mortars.
The Iraqi Insurgency likes to use them, just as they do mortars.
Forgive my ignorance on the subject, but what makes them explode? Is it triggered on impact, or timed (like a grenade)?
Impact, with variable fusing in many cases.
Not always impact. VT fuses can be set to explode in the air over a target.
Gotcha.
¿Qué?
Whoops. VT fuses are for detonation after impact. Proximity fuses are for detonating 1 to 6 meters above ground. Proximity fuses are generally used against troops in the open. VT are used for ground or building penetration.
Shells are fused to detonate in different ways–on entering the ground (artillery or bombs, mostly, not usually mortars), on impact with the ground or other solid object, on very light impacts (like striking a tree limb or camo net–this is called super-quick fusing), or on proximity (a few feet above the ground, to scatter the blast over a wider area).
And let’s not forget Buster Keaton in “The General”…
and
http://www.americanphoto.co.jp/photosearch/Previews/PLX005710.jpg
For the troops taking incoming, the source of pretty much all indirect fire - mortar, howitzer, cannon, free-flight rocketry - is very hard to pinpoint.
However, modern armies can have counterbattery radars that track incoming and compute the position of the firing unit - I’ve heard some boast that they’ll have the counterbattery fire mission transmitted to their own artillery before the enemy shells hit their target. (This is not so much a risk for the company commander’s two 81 mm tubes as it is for the divisional artillery, of course.)
As for why they’re kept around in the age of missiles: Mortar rounds are simple and cheap, compared to missiles. Also, the warhead-to-propellant weight ratio is much, much better - instead of containing an entire rocket motor, the shell just has a powder charge. For infantry units, to whom ammunition is something you carry, this is an attractive attribute in a weapon. (Carrying the mortar itself is, of course, another story…)
This strikes me as a perfect opportunity to mention one of my favourite pieces of weaponry, the Japanese Knee Mortar.
It’s actually not a “knee” mortar, but it had a curved base so that it could be braced against a log or something. Initially, when Allied troops captured them they took the curved base to indicate that it should be braced against the knee or thigh… causing several broken legs.
VT stands for Variable Time, and is a proximity fuse.
My understanding is that the French used mortars to great effect during their intervention into Core D’Ivoire a few years back.
At least in US English, the proper term for the triggering device is “fuze”.
A “fuse” is something totally different having nothing to do with explosives.
Carry on.
As long as we’re being picky, all the dictionaries I consulted disagree with you. “Fuse” is an acceptable spelling for the part of an explosive that ignites first to set off the main charge.
The spelling of “fuze” reminds me that the military takes words and changes the spelling so that the meaning is clear; for example, “fuze”, “alinement” and “orientate”. Dictionaries and thesauruses (thesauri?) don’t exist in an NCO’s list of manuals.
A mortar can also fire an illumnation round, which has a timed “fuze” and a parachute. It slowly falls over the battlefield and lights up the countryside about as well as a streetlamp.
Lastly, I’ve known some operators who we called “mortar-forkers.” 
They were also mounted on small boats during the Civil War, and used to good effect on Western waters: http://www.globalsecurity.org/military/systems/ship/images/mortar-h55826.jpg
Coming in late on this, but it’s Eid and I have some time off. I can say definitively that mortars are most definitely used in conflict in the Third World. I’ve had them fired at me, have supervised their destruction, and have had to call children away from throwing rocks at them to see them go foom.
Mostly 88-105mm, they look like grenades with fins. Nasty buggers that can be rigged as IEDs.
In Saving Private Ryan Capt Miller and Ryan threw mortar rounds at the Germans after striking them against some hard metal plate.
Possible or just film stuff?
One other point no-one has mentioned yet in comparing mortars to rockets is that a mortar has no backblast, whereas it can be uncomfortable to share accommodation with a rocket that is on the point of departure.
Much favoured by the IRA.
1991 - IRA launches mortars at 10 Downing Street while the cabinet is meeting with the Prime Minister.
1994 - IRA launches mortars into Heathrow airport several times.
More examples at Wikipedia.