The Romans did not have, like the Greeks, specific magistrates with oversight of the conduct of women. Censors supervised them only as they did the rest of the republic. The institution of the domestic court  took the place of the magistracy established for the Greeks. 
The husband assembled his wife’s family and judged her in their presence.  This court maintained morality in the republic. But that same morality maintained the court. It was to judge not only violation of the laws, but also the violation of morality. Now for morality to be judged, it must exist.
The punishments of this court were bound to be arbitrary, as indeed they were ; for not everything that involves morality, not everything that involves the rules of modesty, can be included under a code of laws. It is easy to specify by laws what a person owes to others ; it is difficult to include in them all that one owes to oneself.
The domestic court dealt with the overall conduct of women ; but there was one crime which, in addition to correction by this court, was further subject to public accusation : that was adultery, either because in a republic such a huge violation of morality implicated the government, or because the wife’s depravity could cast suspicion on the husband’s, or finally because they feared that even law-abiding men might prefer to hide this crime rather than punish it, ignore it rather than avenge it.