Under classical Roman law marriage without manus was based on consent. With the permission of any relevant guardians a man and woman could declare themselves married as long as both were past the age of puberty, so it seemed not unreasonable that if one of the parties withdrew consent then the marriage was over. Following this principle any man or woman who wished to do so could become divorced simply by sending the partner a letter or even by declaring in front of witnesses that the marriage was over. There was no such thing as joint marital property and any children of the marriage belonged to the father, so there was little to argue about.
If the husband initiated the divorce he had to return the full dowry. Knowing this, the givers of advice, and every society has such people, urged husbands to keep the full dowry in a separate account so they would be able to fulfill this obligation when the time came, for the courts were adamant on the subject. Particularly large dowries were a major impediment to divorce as a high financial penalty had to be paid by the one who initiated it. The bigger the dowry the more power the wife had in the relationship as long as she remained chaste. If the wife (or in some cases her father) initiated the divorce, the husband was allowed to keep one-sixth for each child up to three plus, if applicable, another sixth for her adultery. 
Since children were in the potestas of the father there were fewer custody suits following divorce in Ancient Rome than today. A vindictive man could ensure an ex-wife never saw her children again, and this possibility may well have persuaded some women to remain in an unhappy marriage. If the separation were amicable enough, parents might make private arrangements whereby children, particularly the young ones, stayed with their mother, but if the father wanted them he almost always won, and, of course, wherever the children lived, he remained financially responsible. Nevertheless, there were disputes that went to court. In one case a mother won custody of her child because of the father’s “wickedness.”  In another case a court required an ex-husband to provide child support.  It is likely he denied being the father, and indeed, there were many occasions when a woman discovered herself pregnant after having been divorced. In the absence of modern blood and DNA tests that could establish paternity the Romans had to depend on the calendar. A woman claiming to be pregnant by an ex-husband had to announce the fact within thirty days of the divorce and she could expect to be visited by a group of witnesses sent by him to verify her condition,  for there were instances, or at least men believed there were instances, where vengeful ex-wives passed off a stray foundling as a legitimate son.
The first major change came with the Augustan Marriage Laws. A husband was required to divorce an adulterous wife or face charges of pimping, and the financial penalty against her was increased to half of her dowry and a third of any other property she possessed. On top of that she was then exiled to an island.  We have no way of knowing how well this law was enforced but there was no change in the ability of either partner to get out of a marriage that had not been tainted by adultery.
the Third Century many in
Some have wondered if the influence of
Christianity played a role in this new policy, but most scholars reject the
notion. Christianity’s opposition to divorce sprang up in a society where men
could easily divorce their wives, sending them into the street with little more
than the clothes on their backs, while wives had no ability whatever to get out
of an unhappy marriage. Christianity’s anti-divorce attitude probably arose
from a desire to protect women, while
pressure to make divorce difficult, however, remained, and in 421 the
Theodosian Code declared that a woman who divorced her husband without proving
him guilty of great crimes shall lose her marriage gift and dowry and be
deported for life. If she can prove him guilty of “vices and middling faults”
the deportation order will be lifted but she can never marry again.  This
version of the divorce law applied only in the western half of the Empire, and,
as before, the penalties seem not to have applied to mutually agreeable
divorces. Upset on hearing that there were no penalties for unjustified,
unilateral divorce in the Eastern Empire, Valentinian III in 452 issued a
decree reaffirming the divorce law proclaimed by
The Justinian Code of 449 introduced a number of additional reasons for which a woman in the eastern half of the Empire could get a unilateral divorce without penalty. If her husband plotted to murder her, whipped her, brought prostitutes into the family home or had an affair with a married woman, then a wife could divorce her husband and recover her dowry. In the western Empire it remained almost impossible in law for a woman to get out of an unhappy marriage unless the husband cooperated or she proved him to be a murderer. While we can be quite certain about what the law said on the subject of divorce, the evidence is not at all clear as to what happened in the real world. How many women just walked out of an abusive or unhappy home and left it up to the husband to initiate a divorce if the time came he wanted a new wife? How many times did a husband simply consent when his wife asked for a divorce? In fact, we have no way of even knowing how many people wanted or got a divorce.
 Rules of Ulpian, 6.9
 Digest of Justinian, 126.96.36.199
 Code Justinian, 5.25.3
 Digest of Justinian, 25.3.1
 Ibid, 2.26.14
 Code Theodosius, 3.16.1
 Ibid, 3.16.2
 Novel 35.11 of Valentinian III