The Bible strictly forbids Christians to divorce their spouses, because marriage is sacred. Here is what the Apostle Paul wrote:
To the married I give this command (not I, but the Lord): A wife must not separate from her husband. (I Corinthians 7:10 NIV).
The Apostle Paul gives a clear command here that a wife must not separate from her husband. There is no reason to doubt that this command applies to both sexes: a husband should not separate from his wife either. This means that there is sin involved if a Christian couple gets a formal divorce, or simply decide to separate from each other while still legally married. Paul says that this command does not come from just him, but from the Lord. What he means is that Jesus Christ Himself gave explicit instructions against divorce. However, Jesus also included an exception where divorce is allowed:
“Haven’t you read,” he replied, “that at the beginning the Creator ‘made them male and female,’ 5 and said, ‘For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh’? 6 So they are no longer two, but one flesh. Therefore what God has joined together, let no one separate… I tell you that anyone who divorces his wife, except for sexual immorality, and marries another woman commits adultery.” (Matthew 19:4-6,9)
Therefore, Christians are not to get a divorce, because God Himself has joined them together, and the marriage bond is sacred. However, if one partner commits adultery by having sex with another person, then the other partner is free to get a divorce, because their marriage relationship has already been desecrated. But this does not mean that either party are free to marry another person. Paul says that if a spouse is forced to separate, presumably due to their partner’s sin, that they must either remain single or reconcile with their spouse:
A wife must not separate from her husband. 11 But if she does, she must remain unmarried or else be reconciled to her husband. And a husband must not divorce his wife. (I Corinthians 7:10b-11)
These days people are always looking for an excuse to “move on” from a past marriage if they have been hurt, and want to help themselves heal by finding something new. But I do not think this is Biblical, even if your partner has cheated on you and/or remarried themselves. My opinion, which some good Bible students disagree with, is that death is the only legitimate reason for Christians to remarry someone else. Marriage is so sacred that the vows must be kept even when the other party breaks them.
Having said that, I don’t want to discourage those who have already sinned by divorcing and remarrying someone else. None of us are perfect, we are all sinners, and there is forgiveness for all of us in the blood of Christ. If you are someone who has divorced and remarried, I urge you not to be discouraged, but honor God by loving your current spouse faithfully, and do not let any guilt keep you from satisfying your partner’s sexual needs (I Corinthians 7:3-5). God will forgive you your past sin if you repent of it, but do not add to your sins by neglecting your current spouse. There are many godly couples who have committed the sin of divorce and remarriage before turning to God. You can still honor God through your current marriage if you have committed this sin.