I know that divorce was a thing in ancient Rome, and Julius Caesar divorced his wife (I think) but just how did this process work? Was it anything like modern procedures and were there slightly different methods depending on whether you were a member of the aristocracy, from the provinces, a politician etc.
And in the US about 30% of marriages end with divorce, so do we have any idea what the statistics were for Rome?
Roman law recognized marriages between citizens as existing either cum manu or sine manu, which is to say either with the bride under the legal manus of her husband or distinct from it (generally in her father's familia, unless she was for some reason sui iuris). Marriages sine manu could be quite easily dissolved, since Roman law understood such marriage as a recognition of a pre-existing condition, namely the willful prolonged cohabitation of two individuals bearing conubium. By Roman law the loss of any of these criteria might be grounds for termination of the marriage contract. Naturally lack of will was the most common, and a spouse need only clearly express his or her unwillingness to maintain a stable married relationship for the law to consider the marriage no longer valid. Precisely what constituted a valid declaration of loss of will was not always clear, and the jurists bring up a lot of different arguments and examples, but the theory at least is obvious enough. Little ceremony was required, either for the contract of a marriage sine manu or for its dissolution, which sometimes caused some legal issues when it wasn't always clear if the spouses were really married or not. It's often said that marriages cum manu could not be legally dissolved barring the death of a spouse, but technically speaking this is not true. Several forms of marriage cum manu existed, depending on the precise ritual followed to establish the transfer of the wife from her father's familia into the hosuehold of her husband. The most common was the coemptio, which could not normally be terminated, although by late antiquity the ritual, which involved a symbolic manumission of the bride, had ceased to exist. The other two forms of marriage cum manu were those contracted as confarreatio and as usus. As part of the law of usus a man automatically transferred his wife from her father's familia into his own after exactly one year of continuous cohabitation with her. But manus was only obtained in this way if a woman's cohabitation was truly for a full year--three consecutive days spent outside her husband's bed each year were enough to maintain a woman's status as a wife sine manu. That doesn't have much to do with divorce though, except in that it maintained marriage sine manu, with the freedom to divorce by will alone. Manus marriages contracted by confarreatio involved a highly complex ritual led by the flamen Dialis and was reserved usually for particular people, especially those intended for certain priestly offices (including the flaminate itself). It was not usually terminated, and apparently was illegal for some time (at least for the flamen Dialis to divorce his wife), but Plutarch mentions that Domitian allowed it on one occasion. Some priestly ritual was necessary to dissolve such a marriage, but Plutarch does not describe it other than to say that it was pretty weird and unsettling.
By late antiquity the various rituals pertaining to marriage cum manu had pretty much disappeared, and in some cases manus marriages had been outlawed. As far back as the Republic marriages sine manu made up the vast majority of Roman citizen marriages even among the upper class, and we should expect that manus marriages were almost unknown among the plebs, except in the unusual case of usus, which was probably shaky legal territory for the itinerant day laborers who made up the bulk of the urban plebs. By late antiquity the spouse's declaration of loss of will had been more formalized as a written notice to be delivered and openly declared. Dissolution of marriage remained a difficult legal issue, however, and in 542 Justinian issued an edict that formally laid out the legitimate grounds for dissolution of a marriage. To these he added a number of harsh penalties, such as loss of dowry money and loss of conubium, on top of a series of lighter penalties from the early Principate intended to discourage divorce. Other types of marriage existed, however, and were recognized to varying degrees by Roman law. The ius gentium and the various legal states of subject peoples of the early Principate necessitated that Roman law recognize a wide range of possible marriage contracts, according to the customs and laws of the various subject peoples. And while Roman citizens could not formally enter into full marriages either sine manu or cum manu with non-citizens and other individuals without the right of conubium the law recognized such cohabitation as valid, forming various types of unofficial or lower marriage. For example, concubinatus was, technically speaking, the stable union (which I do not believe required actual cohabitation, although it did require will) with an unmarried citizen man and an unmarried woman of lower status, either a non-citizen or a Latin. Children of the union were not considered legitimate and followed the lower status of the mother, but the status of the union as a sort of marriage-in-kind was maintained according to Roman law.