Islam allows divorce as a last resort, after attempts at reconciliation. A husband can end the marriage by talaq, a wife can ask for a divorce through a judge (khul' or faskh), and in each case there are waiting periods and rights for both sides.
The fuller answer
The Prophet ﷺ discouraged divorce, and the Quran encourages arbitration by family members. After a talaq, there is a waiting period (iddah) of about three months, in which the husband should not throw his wife out of her home, and during which they may reconcile. The wife keeps her mahr, and the father supports the children.
Women have the right to initiate: khul' is a divorce in which the wife returns the mahr, and a judge may dissolve a marriage for harm, neglect or non-support. In practice, in some countries, women face difficulties in the courts, and in some places instant divorce by repeating the word three times is practised even though many scholars and several countries have restricted it.
Divorce is twice. Then, either keep [her] in an acceptable manner or release [her] with good treatment. And it is not lawful for you to take anything of what you have given them unless both fear that they will not be able to keep [within] the limits of Allah. But if you fear that they will not keep [within] the limits of Allah, then there is no blame upon either of them concerning that by which she ransoms herself. These are the limits of Allah, so do not transgress them. And whoever transgresses the limits of Allah - it is those who are the wrongdoers.
O Prophet, when you [Muslims] divorce women, divorce them for [the commencement of] their waiting period and keep count of the waiting period, and fear Allah, your Lord. Do not turn them out of their [husbands'] houses, nor should they [themselves] leave [during that period] unless they are committing a clear immorality. And those are the limits [set by] Allah. And whoever transgresses the limits of Allah has certainly wronged himself. You know not; perhaps Allah will bring about after that a [different] matter. And when they have [nearly] fulfilled their term, either retain them according to acceptable terms or part with them according to acceptable terms. And bring to witness two just men from among you and establish the testimony for [the acceptance of] Allah. That is instructed to whoever should believe in Allah and the Last day. And whoever fears Allah - He will make for him a way out
Divorced women remain in waiting for three periods, and it is not lawful for them to conceal what Allah has created in their wombs if they believe in Allah and the Last Day. And their husbands have more right to take them back in this [period] if they want reconciliation. And due to the wives is similar to what is expected of them, according to what is reasonable. But the men have a degree over them [in responsibility and authority]. And Allah is Exalted in Might and Wise.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.