Voiding a marriage in Islamic law is much more private than it is in Western tradition and does not involve courts. While permitted under Islamic law, it is an act that is said to be frowned upon by Allah and is not to be undertaken lightly. Different sects may interpret some of the fuzzier passages in the Qur'an differently, which affects how much say a woman has in the divorce process. There are no set grounds for divorce, such as adultery or abandonment. That is not the case for annulment.

Talaq

The rules of divorce in Islam are different for men and women. A divorce initiated by a man is called Talaq. One initiated by a woman is called Khula. Men are considered to have far more leeway in divorce than women, but that is subject to interpretation of the Qur'an. Talaq follows a set process in order to be valid. A man must say "I divorce you." This cannot take place during a woman's menstrual period. At that point, there is a set period of about three months, counted by menstrual cycles, called the iddat. During that period, attempts at reconciliation are supposed to be made. If he does not verbally take her back or they don't consummate their reconciliation by the time she is finished her third menstrual cycle, then they are officially divorced. During the iddat, he is not to throw his wife out, nor is she to leave, unless she engages in public scandal. He is to be kind to her and is responsible for supporting his children. If they reconcile or choose to remarry after the first divorce, but have problems later, he may follow the same procedure again for a second divorce. The third divorce is the final divorce, because after the third iddat period is over, she is forbidden to him. They can only remarry again if she marries another man, consummates the marriage and is divorced by him. There are penalties in place to prevent "false" second marriages for the purpose of ex-spouses remarrying, known as Halala. The purpose of this process is to encourage reconciliation by allowing couples to calm down and work through their issues. A marriage to a second person after the third divorce lets a couple explore their relationship to each other through comparison to another. Even though the words "I divorce you" can be said out loud at a moment of anger with little provocation, there is nothing frivolous in Islamic law when it comes to divorce and its desire for couples to stay together. The shortest divorce under Islamic law takes three months and irreversible divorce takes at least nine months.

Khula

Khula, or a divorce initiated by a woman, is not final without approval by the husband. After she announces "I divorce you," the couple must wait through the iddat period, living in the same house together as man and wife, but without having marital relations. However, the iddat period in Khula is just one cycle, or one month, instead of three. If the husband is in agreement, then they are divorced. Any marriage she contracts to during her iddat is considered invalid, since she is not truly divorced until the end of iddat, even if her husband agrees.

Faskh

A woman also has the option to annul her marriage (Faskh) if she can prove to a judge that her husband is an unsuitable partner due to his having a communicable disease, being impotent for more than one year, or her being coerced into marriage by a third party who is not her father or paternal grandfather. She can also ask for an annulment as soon as she turns of age if she was made to agree to an arranged marriage as a minor. Marriages that take place between Muslim women and non-Muslim men, even if it is due to her conversion to Islam, are also subject to annulment.

Source:

Domini.org: The Law and Practice of Divorce in Islam

Islamic Sharia Council: What is the proper way of giving divorce in Islam?

International Law: Annulment of Islamic Marriages