From Tar Valon Library
Compulsion is a weave that forces the victim to feel love and admiration for the person who is using it and to be filled with an overwhelming desire to do as they instruct (TSR, Ch. 46). It is a complex weave of Spirit streaked by Water and Air (TSR, Ch. 54), it can be sliced by spirit (TSR, Ch. 54). During the War of the Shadow, it was a potent weapon. People were forced to serve the Shadow against their will. Others were converted to undercover agents, to betray the Light at the most damaging times (TWoRJTWoT, Ch. 4).
There are limits (TSR, Ch. 46), though these depend on how much of a talent the person has. Compulsion can be unravelled and its effects undone (LoC, Ch. 6). Some people's strength of will and sense of self is so strong that compulsion is never complete and must be reapplied constantly (TFoH, Prologue). Rahvin must do this with Morgase (TFoH, Prologue). When Nynaeve sees Moghedien in Tel'aran'rhiod, she remembers compulsion being used on her (TSR, Ch. 52).
There are many possible uses and variants. Graendal uses compulsion like a hammer, with no subtly leaving little more than fawning servants, incapable of independent action (TFoH, Prologue). She is however capable of using it subtly, so that no trace can be detected (LoC, Ch. 6).
Compulsion in Tel'aran'rhiod is stronger than in the real world (TFoH, Ch. 34). It has many limits, but a command to-do what someone wants to do in their inmost depths will hold for a lifetime. (TFoH, Ch. 34). If used unwisely, a victim could lose a day or more, or be slower of wits (ACoS, Ch. 30). It can be used to give a person false memories (TPoD, Ch. 12).
The White Tower and Compulsion
Compulsion is prohibited by the Tower, even weaves that are similar are not allowed (TPoD, Prologue). Forms of compulsion are a common wilder trick, but it is so strongly discouraged that by the time training has gone long, few can remember much about it (TPoD, Prologue). Theodrin had this (LoC, Ch. 8) and Liandrin knows a simple version, that makes a person more easily persuaded (TFoH, Ch. 34). She uses her weak form on Amalisa to force her to help search for Rand (TGH, Ch. 5). Verin pieces together a rough form of compulsion from weaves novices half remembered (TPoD, Prologue). It makes a person more susceptible and she uses it to persuade the Aes Sedai captives to swear to Rand. Emotional vulnerability helps and trust is essential. The Blue Ajah has a weave that is in some ways similar to compulsion, but is limited to planting a suggestion in a person's mind (NS, Ch. 23).
Egwene believed that Rand might have used compulsion on the captures sisters, to Pevara, that was forbidden so the possibility didn't occur (Robert Jordan’s Blog; Friday, January 20, 2006). She turns down the suggestion of altering the warder bond to bond Asha'man as it is too like compulsion (CoT, Ch. 30).
It is one of the weaves that Elayne and Nynaeve learn form Moghedien but do not pass on (LoC, Prologue).