Biblical Grounds for
In the Old Testament, in the Torah to be exact, Moses makes it clear that a man may divorce his wife because of her "indecency".
 
Deut 24:1  "When a man takes a wife and marries her, and it happens that she finds no favor in his eyes because he has found some indecency in her, and he writes her a certificate of  divorce  and puts [it] in her hand and sends her out from his house...

This "indecency" is NOT adultery, because the penalty for adultery, under the Law (Torah) was DEATH! 

  •   ...the adulterer and the adulteress shall surely be put to death. (Lev 20:10)
  • If a man is found lying  with  a married woman, then both of them shall die... (Deut 22:22)
  • ...Teacher, this woman has been caught in  adultery , in the very act.  Now in the Law Moses commanded us to stone such women... (John 8:4-5)
Therefore, this indecency was some kind of sexual sin LESS than the act of adultery itself!
We see this same rule applied to divorce in the New Testament.
 
Matt 5:32  but I say to you that everyone who divorces his wife, except for [the] cause of unchastity, makes her commit adultery; and whoever marries a divorced woman commits adultery.

Matt 19: 9  "And I say to you, whoever divorces his wife, except for immorality, and marries another woman commits adultery." 

We see another allowance for divorce in the New Testament.
 
1 Cor 7:12  But to the rest I say, not the Lord, that if any brother has a wife who is an  unbeliever , and she consents to live with him, let him not  send  her away.  13  And a woman who has an unbelieving husband, and he consents to live with her, let her not  send  her husband away.  14  For the unbelieving husband is sanctified through his wife, and the unbelieving wife is sanctified through her believing husband; for otherwise your children are unclean, but now they are holy.  15  Yet if the unbelieving one leaves, let him leave; the brother or the sister is not under bondage in such cases, but God has called us to peace.  16  For how do you know, O wife, whether you will save your husband? Or how do you know, O husband, whether you will save your wife?

We see here that if we are already married to an unbeliever, and THEY leave US, we are no longer bound to them.

These two are the only grounds for divorce that this author has found in God's Word.  If you have found others, kindly e-mail me with the references so they may be included here as well.
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Divorce
Adultery
Marriage According to the World; 
Adultery According to the Lord
Who Can Remarry?

Questions? Comments?

Footnotes:

Strong's #3748  kerithuth - translated "divorce" 4 times

Strong's #6172. ervah (788d); from 06168 ; nakedness :-- bare(1), indecency(1), indecent(m)(1),
nakedness(48), shame(m)(1), undefended parts(m)(2).

Strong's #4202. porneia, aV porneia; from 4203 ; fornication :-- fornication(4), fornications(2),
immoralities(1), immorality(16), sexual immorality(m)(1), unchastity(1).