Under the Mosaic Law adultery carried the death penalty by stoning for the woman.
In Jesus' day, confusion prevailed about the grounds for divorce. Even the rabbis could not agree on what constituted the "uncleanness" of (Deut. 24:1). Followers of Rabbi Shammai felt adultery was the only grounds for divorce. Those who followed Rabbi Hillel accepted many reasons, including such things as poor cooking.
The gospels record four statements by Jesus concerning divorce. In two of these He allowed divorce in the case of adultery. In (Mat. 5:32) Jesus commented on the situation of both the woman and her new husband: "Whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery." In another statement, Jesus says "Whoever divorces his wife except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery" (Mat. 19:9). Two other statements of Jesus appear to make no provision for divorce (Mk. 10:11-12; Lk. 16:18).
Jesus' statements in Mark and Luke were made in conversations with Pharisees about the Mosaic Law, which they believed allowed divorce on grounds other than adultery (Deut. 24:1-4). Jesus' main point in these statements was that divorce is contrary to God's plan for marriage and should never be taken lightly.
In the case of sexual unfaithfulness, the decree of divorce simply reflects the fact that the marriage has already been broken. A man divorcing his wife for this cause does not "make her an adulteress," for she already is one. Thus, divorce on the grounds of unchastity frees the innocent partner to remarry without incurring the guilt of adultery (Mat. 19:9). See (Nelson's Illustrated Bible Dictionary)(Copyright (C) 1986, Thomas Nelson Publishers)
In the case of two Christians Paul admonished them to follow the Lord's teachings and be reconciled. In any event, neither is to marry another (1 Cor. 7:10-11). In 1 Corinthians 7:15, Paul says that a Christian who is abandoned is free to formalize the divorce and remarry: "If the unbeliever departs, let him depart, a brother or a sister is not under bondage in such cases."
Practicing pagan/hostile to Christianity
On two occasions divorce was insisted on. These were when the returned exiles had married pagan wives (Ezr. 9-10 and probably Ne. 13:23ff.,) In Mal. 2:10-16 some had put away their Jewish wives so as to marry Pagans.
Moses allowed divorce because of the "hardness" of the spouses heart (Mark 10:5).
Paul stated that we should not be "unequally yoked" with unbelievers (2 cor 6:14).
Paul encourages the believer to keep the marriage together if the unbeliever "consents" or "is pleased to stay," in hopes that the unbelieving spouse might be saved and the children will grow up knowing God. (1 Cor. 7:15-16).
However; if the spouse is hostile to Christianity constantly causing trouble for you and others we have the OT example of putting them away.
Married within the prohibited degrees
If after marriage you find you have unknowingly married a son, grandson, daughter, granddaughter, sister, brother, nice, or nephew (Lev. 18-19) the law of Moses would compel the two to divorce.
Some have doubted the authenticity of Mk. 10:12, since a Jewish wife could not normally divorce her husband. But a wife could appeal to the court against her husband's treatment of her, and the court could compel the husband to divorce her. See (The Illustrated Bible Dictionary)(Copyright (C) 1980, Inter-Varsity Press)
1 Timothy 5:8 And whoever does not provide for relatives, and especially for family members, has denied the faith and is worse than an unbeliever. (NRSV)
Eph. 5:28-29 In this same way, husbands ought to love their wives as their own bodies. He who loves his wife loves himself. 29 After all, no one ever hated his own body, but he feeds and cares for it, just as Christ does the church-
If a husband physically abuses his wife he is not "taking care of" or "providing for" his family, thereby denying the faith and is apparently not "pleased to live with you." If a wife allows her children to be abused if she can prevent it, she is "not providing for her family."
If a man believed that his wife was not a virgin when he married her, he could have her judged by the elders of the city. If they found her guilty, she could be put to death (Deut. 2:13-21). There are two situations where divorce was forbidden: when a man has falsely accused his wife of premarital unfaithfulness (Deut. 22:13-19); and when a man has had relations with a girl, and her father has compelled him to marry her (Deut. 22:28-29; Ex. 22:16-17).
The Law of Moses allowed a man to divorce his wife when she found "no favor in his eyes, because he has found some uncleanness in her" (Deut. 24:1). The primary purpose of this legislation was to prevent him from taking her again after she had married another man- "an abomination before the Lord" (Deut. 24:4).
The only other possible interpretation for "some uncleanness in her" might have been if she came down with a disease like leprosy. Being as good as dead with no hope of being cured and being put in a leper colony.
A public document known as a "certificate of divorce" (apostasy grk.) was granted the woman. This permitted her the right to remarry without civil or religious sanction. Divorce could not be done privately.
Remember that non of these situations force you to divorce. The best option is, if possible, to reconcile.
Other sins against marriage, which are not grounds for divorce, are:
1 Peter 3:7 A hostile attitude (not speaking, threats) to your spouse hinders your prayers.
1 Corinthians 7:5 Not satisfying the sexual needs of your spouse.
1 Corinthians 7:3,4 Not dressing or acting in ways that please your spouse.