Deuteronomy 24:1–4, Here are Natan’s notes on the biblical reasons for divorce.

• Jeremiah 3:14, After YHVH divorced Israel (v. 8), he was still married to her. What’s going on here? Even though YHVH divorced Israel, he still considers himself married to her because he had made a covenantal vow with Israel, and vows can’t be broken (except by death or under very stringent requirements). Period.
• Look at Hosea 1:2 cp. 3:1–3. Hosea’s actions toward Gomer, his adultrous wife, is an example of YHVH’s unfailing love for is Israel, who was his adulterous wife. Marriage is a covenant vow that when broken by adultery requires the death penalty for the offending party. Gomer committed adultery. Yet Hosea brought her back and redeemed her from adultery. He loved her unconditionally and laid his life down for her (as YHVH does for us, see Eph 5:28).
• Deuteronomy 24:1 can’t be used as a justification for divorcing under just any circumstances. Only if the wife has committed or is committing sexual immorality (in Hebrew ervah) can her husband put her away. A bill or divorcement, Hebrew called a get, must first be issued for the purposes of restoring the immoral woman. One can’t put their wife away for any reason. Even Yeshua confirmed this in Matthew 5:32. Ideally, according to the Torah and to Yeshua some sexual immorality or ervah has to have been committed for a man to divorce his wife.  I inserted the word ideally because there are seldom ideal situations in life, and humans rarely live up to YHVH’s ideal moral and spiritual standards. As such, Yeshua admits that the Torah as administered by Moses allowed for divorce to occur because, sadly, of the hardness of human hearts (Matt 19:8). What does “hardness of heart” mean?  Scripture doesn’t say. The following is simply my speculation on what this means. I would not expect one to be required to stay married if several severe conditions existed such as physical abuse, criminality, drug addictions, abandonment, total dereliction of responsibilities or extreme heathenism. Such sins make it all but impossible for a righteous person to remain in such a spousal relationship. A spouse who is practicing such has violated their contractual marriage vows and thus there legally and technically is no marriage. A believer shouldn’t be forced to remain in such a relationship. Having said this, it is the saint’s duty to vet out as much as possible a prospective mate before marrying them to ensure that they have never been involved and are not currently involved in such activities. One should only marry an Elohim-fearing, commandment-keeping faithful believer in Yeshua the Messiah, who has a long fruit-bearing track record of such a lifestyle. Again, this is Natan Lawrence speaking, not Scripture, but it is my best understanding of scriptural principles as they relate to marriage and divorce.
• Marriage between two believers and is a vow with YHVH. Marriage between two unbelievers is something else. It’s simply an agreement or contract between two people. Maybe YHVH is part of it, maybe he is not. It all depends on the vows and the situation. 
• Deuteronomy 24 is not a permission to divorce and to remarry. Rather it is a judgment because of sin. It must be viewed in manner. YHVH’s Torah-laws, statutes and ordinances are for when things go well. The judgments of Torah, on the other hand, were for when things went wrong. A judgment was meted out because some Torah-law had been broken and now a solution to the problem had to be found or worked out within the framework of Torah. This is the situation Deuteronomy 24 is dealing with respect to marriage covenant that has been violated. A get was a temporary legal measure to protect the adulterous woman from stoning so that the marriage could be restored.
• In the Torah, divorce was to be a temporary situation to bring the sinning wife to repentance and to restore YHVH’s perfect ideal of marriage—to restore order back into the home, to heal the family structure. If the sinning wife refuses to repent and remarries (Deut 24:2–3), and continues in her sin and she’s divorced again or her second husband dies, this is what servers the marriage covenant permanently. This act on her part renders the marriage covenant null and void forever.
• Again, a bill of divorcement or a get under the Torah was a temporary legal measure to protect the adulterous woman from stoning, so that the marriage could be restored. Matthew 1:19 demonstrates this. Joseph acted righteously in not putting Miriam (Mary) his pregnant betrothed wife away, which could have resulted with her being stoned to death. By all outward appearances, she was guilty of adultery, but Joseph’s act of mercy was an example of his exercising mercy over judgment. In ended up that she was pregnant not by a man, but by the Spirit of Elohim resulting in the birth of Yeshua the Messiah. Thus Joseph’s act of mercy spared the Messiah from potential death.
• In Malachi 2:10–17 YHVH addresses the issue of divorce. Here is discussing the treacherous nature and misuse of divorce, which is one of the reasons he states that he hates divorce (v. 16). This is because divorce often results in treacherous dealings between people (vv. 10–11, 14) and it violates and profanes sacred covenants (vv. 10), it profanes the holy institution of marriage, which YHVH loves (v. 11), because it’s often the result of adultery (vv. 11–12), and adultery leading to divorce often causes a man to leave the wife of their youth (v. 14) thus breaking the oneness of marriage (v. 15), and divorce covers one’s garments with violence (v. 16). Again, for these reasons, YHVH hate’s divorce, and why he refers to it as “evil” and unjust (v. 17).
• According to YHVH’s Torah standard, we’re to care for widows and orphans, not to create them as a result of the misuse of Torah’s laws regarding divorce.
• In Matthew 5:32 Yeshua’s words fit into the above context. Only, ideally under strictest standards of the Torah, for sexual immorality is divorce permissible. Otherwise divorce is unlawful, since the couple is legally still married and a bill of divorce (a get) is simply a temporary measure for purposes of reconciliation the couple and bringing the marriage back together.
• In Matthew 19:3, when Yeshua mentions divorce “for just any reason,” he is referring to the Pharisaical schools of Beit Shamai and Beit Hillel of the time. The Pharisees that came to him asking the question were from School of Hillel. Yeshua is taking the Beit Shamai conservative position as the case when John the Baptist took Herod to task for his adultery. Verse 8 shows that there’s a provision for divorce but it’s not YHVH’s perfect will. Rather it’s a judgement and an indictment against carnal men.
• Again, in 1 Corinthians 7:10–11, we see that the primary purpose of divorce is for reconciliation of the marriage, not so that one can justify themselves in getting out of a less than ideal marriage in order to fetch themselves another spouse. Divorce and remarriage, as millions of people will attest to, causes a shipload of unintended negative consequences on the lives of many people and often for generations to come. It is something to be avoided if at all possible.