Gholam are immune to the One Power and most known weapons. They can detect a channeler at fifty paces and someone holding the One Power from even further. From several miles away gholam are able to feel use of the One Power and True Power as an itch akin to that experienced by the Myrddraal.
Gholam live on fresh blood, generally rending their victims limb from limb or tearing their throats out before feeding. Their preferred prey are channelers, as they receive a sense of euphoria when they take the life of one who can channel.
Furthermore, gholam are incredibly resistant to harm. They are completely immune to conventional weapons and weaves directed at gholam dissolve. However, they may be indirectly harmed by weaves that are directed at other objects or at the surrounding environment. At the present time, the foxhead medallion worn by Matrim Cauthon is the only thing known to have hurt a gholam.
They possess a degree of superhuman strength, and one can easily tear a man's throat out with it's bare hands. While attempting to resist one strength-to-strength, Matrim Cauthon mentally compared the contest to a child attempting to resist the strength of a grown man, and that comparison was made while the gholam was merely toying with him. Additionally, the one that Mat fought in Ebou Dar was noted by him to be even faster than a Myrddraal. Due to the fact that they lack any sort of skeletal structure, they are impossibly flexible and agile, and can squeeze through incredibly small spaces. They can also apparently survive going through a gateway.
The final gholamEdit
It looks like a man, slender with sandy hair and unremarkable features. It has a scar on its cheek where Mat hit it with his foxhead medallion.
Ebou Dar Edit
The gholam began its killing spree with Herid Fel, a knowledgeable resident of Rand al'Thor's school in Cairhien who had been helping Rand figure out what to do about the seals to the Dark One's prison.
It was then sent to Ebou Dar to attempt to stop the recovery of the Bowl of the Winds. There, it attacked a number of Wise Women, Elayne Trakand, Mat, and his Redarms. It fled after touching Mat's medallion, which appeared to burn its cheek.
It demonstrated independent thought, as it had been ordered to track down Nynaeve al'Meara and Elayne but it wanted revenge on Mat for hurting it. It attacked Mat again in Ebou Dar, and was again forced to retreat when Mat defended himself with the medallion and Noal Charin came to his aid. It remained in Ebou Dar killing arbitrary people for their blood. In its hunt for Mat, it also killed Queen Tylin Quintara Mitsobar after finding her in chambers where Mat had left her tied up when he left Ebou Dar.
After the Band of the Red Hand set up camp a league outside Caemlyn, the gholam returned, now under orders to kill Mat and those close to him, like Thomdril Merrilin, Noal, and Tuon. It left a trail of dead citizens in Caemlyn as it tracked him, finally coming to wait for him at the Band's camp, where it killed Lopin before attacking Mat again. It would have succeeded if not for the aid of Teslyn Baradon. It was eventually forced to flee after the rest of the Redarms were alerted. 
Soon afterward, Mat confronted the gholam for one final time, intentionally luring the creature to him in the streets of Caemlyn. He surprised the gholam with two extra foxhead medallions, lesser copies created by Elayne, and backed the Shadowspawn into a house. Then he used the three medallions to dispose of the gholam by corralling him into a gateway leading to the endless void used for Skimming, which had been carefully placed beforehand by Sumeko Karistovan. He then pushed it off the edge where it would fall through the void until it died. 
Etymology and TriviaEdit
The word gholam is likely a reference to golem, an animated anthropomorphic being made of inorganic matter that appears in Jewish mythology and popular culture.
While it's final fate was not discussed in the novels, Brandon Sanderson stated in an interview that, while going through a gateway would not kill a gholam, a few minutes spent inside the dimension used for Skimming would, and indeed the one that Mat confronted died after a few minutes of falling through the void of the Skimming dimension.