It all depends on the reasons for the divorce. Jesus brought up the subject just as one example of situations which Moses allowed under the Law, and the more strict requirement of righteousness that Jesus pointed out. In one session where Jesus was showing that our righteousness has to exceed the righteousness of the Pharisees (who incidentally were so strict concerning observance to the law, were to all intents and purposes, blameless), Peter exclaimed, "Who then can be saved?" Jesus' reply was that with man it is impossible, but with God all things are possible. If Jesus had not been pressed by the Pharisees, He would not have mentioned divorce and remarriage at all, and His comments about it were not intended to be viewed as hard and fast doctrine, as some "churchians" suppose. Also, Jesus was speaking to Pharisees and not to the common people.
There are those who are steeped in "churchianity" who would revictimise a woman who has had to flee a marriage to a violent, homicidal husband, to save her life and that of her children. Also for a spouse who has been deserted with no hope of reconciliation. Gambling or boozing away the household income causing the spouse and children to starve, be thrown out of their home because of unpaid rent, or mortgage sale, repossession of appliances and furniture, would require a spouse to divorce for the sake of their well-being. Jesus never went into the different causes of why people get divorced because it was not relevant to the discussion He was having with the Pharisees at the time. Nor would these reasons were relevant to Paul's teaching to the Corinthians, because the reason why he gave the teaching was because men were putting away their wives for the sole reason that they wanted a closer spiritual relationship with God, and they believed that celibacy was the answer. Paul taught that the marriage contract depended on wives loving and being submitted to their husbands, and the husbands loving their wives as Christ loved the church. When a spouse fails in that respect, the marriage contract is broken, and if a responsible spouse refuses to repent, then he or she in effect becomes an unbeliever, and Paul says that a person doesn't have to remain married to an unbeliever, the believer being either unconverted, or who has made him or herself an unbeliever through disobedience and refusal to accept correction by the Church.
If a spouse is adulterous, violent, deserting the marriage, a gambler, or alcoholic, and will not submit to correction by the elders of the church, then he is to be treated as an unbeliever and put out of the fellowship until he or she repents. I believe in that case, the innocent spouse is free from any obligation to the marriage and has the freedom of choice whether to stay that person or to be divorced without any penalty from God or the church. And if reconciliation turns out to be totally impossible, be free to remarry without penalty.