Going to elaborate on a previous answer I gave here.

Were elephants used in war for a long time? Yes. Were they giant invulnerable tanks that could slaughter lines of infantry? Not really. The problem with elephants is that despite being huge, they are just as sensitive and fearful as any other animal, and will be frightened by javelins, horses and just the loud noises and general panic of a large battle. Elephants could be and were used to break infantry formations, but no mahout would ever try charging a line of spears, as this would probably cause the beast to panic. The biggest issue with elephants in battle was what happened after they panicked, as they would usually run amok, crushing friend and foe alike. In fact, their mahouts had to carry chisels to drive into the skull of their animal in case this happened. Having said that, a skilled commander could use elephants to great effect. Elephants were effectively monsters to the ancients, and would terrify less experienced soldiers and other animals. While you would never open a battle with a charge, once the enemy has been softened up there was no way to really stop an elephant that didn't involve lots of men being trampled, but because of how tall they are they were often used as mobile archery towers instead of right on the front line. This hesitance to risk them is also due to how rare elephants actually were. Even in regions were the animals were not uncommon, the loss of multiple elephants would be devastating to an army, as it it takes a lifetime to train these animals, and complicating matters, the females and young males can't be used in battle against other elephants, as mature bulls intimidate other elephants.

The main strength of war elephants was undoubtedly their effect on the enemy's morale. Elephants, especially large indian elephants of the ancient era (used mostly by the successor states of Alexander's Empire), are large, scary and noisy. Additionally, their unfamiliar smell and sound is known to make enemy horses panic.

War elephants are an all-purpose unit. Hellenic war elephants usually had a structure mounted on their back, manned with ranged units (javelin throwers or archers), protected from enemy attacks. Additionally, their elevated position provided them an excellent overview of an enemy army and a considerably greater range of attack.

In addition, the elephant itself was a melee destructive force. It was without any doubt the strongest entity on any ancient battlefield, and could trample and mow down any soldier in their way (with swords attached to their tusks). They were usually large males, filled with aggresion and testosterone, and they were very often drunk.

Before the battle, war elephants were usually given a generous amount of wine, (and they were very happy to drink it). That had a very similar effect on them to what alcohol has on humans, and it multiplied their agression and strength, reduced their sense of fear and made them ignorant of pain.Their drunken rage must have been terrifying for both foes and friends on the battlefield.

One follow-up:

I've seen pictures from the Pacific theater in WW2 where elephants are being used as tractors, essentially, in jungles for clearing roads, building bridges, and so on.

Did ancient armies do anything similar? /u/elephantofdoom mentioned how females and young males couldn't be used in battle, I'm wondering what other uses they might have had