Thanks so much for writing. The question you've posed is a complex one that we will be able to examine only briefly here; sadly, most people today -- including Christians -- either do not ask this question or willfully ignore its biblical answer.
In the first place, we must note that God never intended for husbands and wives to divorce. He allowed divorce under the Mosaic law not because divorce was His design but, rather, "because of the hardness of (Israel's) hearts" (St. Matthew 19:8). Divorce exists on account of our sin, not on account of God's desires for us. The Lord says plainly He hates divorce (Malachi 2:16), and for good reason: divorce violates God's original intent for the intimate covenant of marriage.
We nonetheless must concede that the Scriptures allow for divorce in two instances: fornication/adultery and abandonment. In limiting "biblical" divorce to these two categories, the Lord is invalidating "incompatibility" or "we just grew apart" (among others) as excuses for divorce.
Regarding fornication (or sexual immorality), this sin obviously includes situations in which one (or both) marriage partners defiles the marriage bed by having intercourse with an outside party. The Greek term "porneia," however, also seems to include *any* illicit sexual activity.
One might raise the question, "Does the use of pornography by one partner entitle the other partner to divorce him/her biblically?" This issue is clearly more complex than the one explicitly involving intercourse, and the couple would need to work through the situation carefully and prayerfully with their minister. As evil as are pornography and its use, we always must remember that God's design is for joyous, healthful, pure marriages -- and that He can work through difficult circumstances to bring healing and transformation through Jesus Christ. He wants the couple's whole hearts to be given to Him -- and for their love for one another to be undivided and pure. Thus, while the use of pornography taints the marriage bed, it need not continue, nor must it signal the death-knell for a marriage.
The other allowance for divorce is found in I Corinthians 7, in which St. Paul allows the "abandoned" spouse to divorce the other, unbelieving party. Certainly some cases of abandonment by an unbelieving spouse (or one who shows him/herself to be an unbeliever) are clear-cut. Other instances are somewhat more clouded, and again, the couple -- or concerned spouse -- would be wise to work through the situation prayerfully with his or her minister and elders. Suffice it to say, however, that desertion/abandonment does NOT include such issues as "we just grew apart" or "we wanted to do different things in life" but POTENTIALLY includes such sins of abandonment as abuse, wanton behavior and general, prolonged, unrepentant abdication of one's marital responsibilities. Abandonment need not be restrained to literal physical desertion; but it must not be expanded to include every concocted "reason" for divorce in our modern world.
Paul reminds us in I Corinthians 7 that we are to seek peace with one another and to have the salvation of others, and the glory of God, ever in the forefront of our minds. This means divorce should be the option of last resort for Christians, and that only in legitimately (i.e. by the evangelical, Bible-preaching church) recognized and irreconcilable cases of adultery and abandonment. In all things, we are to stand apart from the world while yet living in the world, and we are -- whether married or not -- to live for the glory of God at all times and in all places.
May the Lord bless our marriages!