At this point I have to set out some important caveats.
My primary expertise, both as a poet and a linguist, concerns modern English. I do not consider myself a specialist in older forms of English. And indeed, my interest in alliterative verse focuses on the possibility of writing alliterative poetry in modern English, not in establishing the precise details of older forms of English (or any other language.)
I think I have gotten a fairly accurate picture of alliterative verse from my reading in the scholarly literature. But I will leave detailed explanations of exactly how medieval poetry worked to the specialists. What follows is intended first and foremost as a poet's guide to writing similar verse in modern English.
That means that much of what I say in following sections has to be read in a double light. I will try, as much as possible, to make what I say applicable to the older, medieval forms. But I will feel free to offer my opinion about points of detail based upon my assessment of what works for a poet writing at the turn of the second millenium.
In other words: what follows is my best personal summary of how medieval alliterative poets would have composed their poems if they were writing in English right now.
As part of that process I will evaluate various poets who have imitated alliterative verse, or claimed it as an inspiration. It turns out only a few of the poets who have attempted modern alliterative verse have come close to the classic medieval forms. Most of the work that claims to be inspired by Anglo-Saxon or medieval alliterative verse is a very loose imitation indeed. But more of that anon.