According to all four schools of Sunni law and Shia law, interfaith marriages are condoned only between a Muslim male and a non-Muslim female from the People of the Book (that is, Christians and Jews) and not vice versa.
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Marriage of Muslim men to non-Muslim women
Islamic marriage rules between Muslim men and non-Muslim women are regulated by Islamic principles. There are restrictions to whom a Muslim man can marry. Muslim men are forbidden from marrying polytheist women. A polytheist woman would have to convert to Islam if she would want to get married to a Muslim man, according to Islamic principles.
Marriage of Muslim women to non-Muslim men
(See verse 60:10 below)
Muslim women are forbidden from marrying non-Muslim men according to Islamic law. There also exists a minority view that does permit women who have converted to Islam to remain with non-Muslim spouses as an exception to the general rule. This minority view is however restricted to converted women only.
Conversion to Islam of one spouse in a non-Muslim marriage
Under Islamic law, if a non-Muslim woman is married to a non-Muslim, and she converts to Islam, the marriage is suspended until her husband converts to Islam. She could, in theory, leave the non-Muslim husband and marry a Muslim one. If the non-Muslim husband does convert a new marriage is not needed. In the Quran, it is said,
O ye who believe! When there come to you believing women refugees, examine (and test) them: God knows best as to their Faith: if ye ascertain that they are Believers, then send them not back to the Unbelievers. They are not lawful (wives) for the Unbelievers, nor are the (Unbelievers) lawful (husbands) for them. But pay the Unbelievers what they have spent (on their dower), and there will be no blame on you if ye marry them on payment of their dower to them. But hold not to the guardianship of unbelieving women: ask for what ye have spent on their dowers, and let the (Unbelievers) ask for what they have spent (on the dowers of women who come over to you). Such is the command of God. He judges (with justice) between you. And God is Full of Knowledge and Wisdom. {Surah 60:10}
Modern practice
In practice, many Arab countries allowed interfaith marriage to Christian or Jewish women but not to non-Muslim men. In Lebanon for example there is no civil personal status law and marriages are performed according to the religion of the spouses. There, Muslim women cannot marry non-Muslim men, whereas this is possible vice versa, at least if the spouse is a Christian or Jewish woman. Turkey allows marriages to non-Muslim men through secular laws. In Malaysia a non-Muslim must convert to Islam in order to marry a Muslim. The offspring of such unions are automatically Muslims and all Malaysian Muslims are legally prohibited from leaving Islam (Riddah).
Interfaith marriage especially between Hindus and Muslims often have been the bone of contention and have resulted in communal riots in India. Love Jihad, also called Romeo Jihad, widely regarded as a conspiracy theory, is an alleged activity under which young Muslim boys and men are said to reportedly target young girls belonging to non-Muslim communities for conversion to Islam by feigning love. Official investigations in Uttar Pradesh had found no credence in allegations of Love Jihad that had been brought before them, with state police chief A.L. Banerjee stating that, "In most cases we found that a Hindu girl and Muslim boy were in love and had married against their parents' will.