The most consequential dispute over Buddhist ordination today is whether women can receive full ordination in traditions where the female lineage has lapsed. It turns on a technical point with very large effects.
The lineage requirement
Valid higher ordination is held to require an unbroken chain: those who ordain must themselves have been validly ordained, back to the early sangha. For the full ordination of a nun (bhikkhuni), the tradition further requires that the ceremony involve an existing order of bhikkhunis. This is the knot. In the Theravada the bhikkhuni lineage died out around the eleventh century, and in Tibetan Buddhism a full bhikkhuni lineage was arguably never established at all.
The two positions
It cannot be restored. If full ordination requires ordained bhikkhunis, and there are none in the lineage, then the chain is broken and cannot be repaired from within it. On this view the most that women can hold is a lesser, informal renunciant status, the Thai mae chi, the Burmese thilashin, which is not full ordination and does not carry its standing.
It can be restored. The East Asian bhikkhuni lineage, in the Dharmaguptaka tradition, has survived unbroken. Reformers argue that this surviving lineage can supply the required bhikkhunis, and full ordinations of women drawing on it have taken place since the late twentieth century, a landmark ordination in Bodh Gaya in 1998, and continuing ordinations in Sri Lanka and elsewhere. Opponents question whether a lineage from a different school can validly confer Theravada ordination.
Where it stands
Unsettled, and institutionally charged. Bhikkhuni ordination is now a reality in Sri Lanka and among Western practitioners, and is accepted by some senior figures and rejected by others; in Thailand the official monastic hierarchy has resisted it. The scholar-monk Bhikkhu Analayo has argued at length that the revival is compatible with the monastic code, and the argument continues on textual as much as institutional grounds. It is a live question in a living tradition, not a settled rule.