When is divorce forbidden, permissible, neutral, recommended, or obligatory, especially if the wife insists on it?

A woman is not permitted to seek divorce without a valid reason, based on the Prophet's (peace be upon him) saying: "Any woman who asks her husband for divorce without a sound reason, the scent of Paradise will be forbidden to her." As for the ruling on a husband divorcing his wife, it varies according to the motive: it can be obligatory, such as divorcing a husband who has sworn off sexual relations with his wife (mu'li) after the waiting period; it can be disliked (makruh) if there is no need for it; it can be permissible (mubah) when there is a need due to the wife's bad character; it can be recommended (mandub) if the wife neglects her duties towards God; and it can be forbidden (mahzur), such as divorcing during menstruation.