The passages in the New Testament that address this issue are Matthew 5:31-32; 19:1-12; Mark 10:1-12; Luke 16:18; 1 Corinthians 7:10-16; and Deuteronomy 24:1-4 in the Old Testament is important background. This is quite a tricky question to answer because of the brevity of the comment in Deuteronomy (and it is focused on one specific situation), because of cultural understandings of divorce in the New Testament period, and also because only Matthew out of all the gospel writers includes the “exception clause” (Matthew 19:9). Therefore, Christians do have different views on this issue (for example, John Piper would argue that divorce and remarriage is never permitted).
Jesus’ answer about divorce in Matthew 19
We’ll focus on Matthew 19 since this seems to be the fullest account. In it, the Pharisees come to Jesus and ask “Is it lawful to divorce one’s wife for any cause?”. Jesus’ answer goes back to the creation account and God’s original intention for marriage in Genesis 1 and 2. Jesus quotes Genesis 1:27 (the Creator “made them male and female”) and 2:24 (“therefore a man shall leave his father and his mother and hold fast to his wife, and the two shall become one flesh”). Next, He underlines that fact that when a man and woman are married they “are no longer two but one flesh. What therefore God has joined together, let not man separate” (Matthew 19:6).
But what about Moses?
Therefore, Jesus’ basic answer is that in marriage a man and woman are united/joined together by God – they become one flesh – therefore, they should not be separated (i.e. the shouldn’t get divorced). However, the Pharisees then ask another question: “Why then did Moses command one to give a certificate of divorce and to send her away?” (Matthew 19:7). The Pharisees are referring to Deuteronomy 24:1, where Moses allows a man to give a certificate of divorce to his wife. Why then does Moses (who is speaking God’s words, not his own) allow divorce when God in Genesis 1 and 2 seems to forbid it?
Jesus’ answer is that it is “because of your hardness of heart” (Matthew 19:8), that Moses (speaking God’s words) permitted divorce. It is important to remember at this point that between Genesis 1 and 2 and Deuteronomy 24, an enormous tragedy took place: Adam and Eve disobeyed God’s command. As a result, God has judged them and they are no longer permitted to live in the Garden of Eden. People’s hearts are now hardened. Therefore, although a man and women still become “one flesh” when they are married, God now permits divorce in certain situations. (Another way of looking at this is that in Genesis 1 and 2 divorce would have never been an issue, since a husband and wife would never have sinned against each other in any way, but that after Genesis 3 sin and divorce do become issues.)
Adultery
Jesus’ verdict in Matthew 19:9 is: “whoever divorces his wife, except for sexual immorality, and marries another, commits adultery.” Therefore, Jesus allows divorce only in the case of sexual immorality (how this is to be understood exactly, is still a topic of debate among Christians). In 1 Corinthians 7:15, Paul is also addressing the topic of divorce. He is talking about marriages where one spouse is a Christian and the other is a non-Christian. In 1 Corinthians 7:12-14, Paul says that if the non-Christian spouse is willing to continue living with the Christian, then the Christian should not divorce. However, if the unbelieving spouse leaves the marriage, then the believing man or woman is not bound (1 Corinthians 7:15). In such a situation, the Christian who is left by his/her spouse does not sin if he/she accepts the situation of the divorce as initiated by the other partner.
Marriage is a very high calling
In summary: marriage is a very high calling, in which a man and woman, when they are married, become one flesh – God joins them together. Therefore, they should not separate/divorce. However, if there is unfaithfulness within the marriage, then there can be divorce (there doesn’t have to be however; the couple might (ideally) show forgiveness and grace and the marriage continue!). Also, in a marriage between a Christian and non-Christian, if the non-Christian leaves the marriage, then the Christian is not sinning if he/she accepts this situation.