Give us a bit more info if you can John,
It looks to me as though it's an oldish, (is it plasterboard or lath? ) ceiling that was plastered, (floated and set) some years ago, and because of the lack of key on the float coat, the finish coats have parted company with the undercoat,,, or,,
someone has skimmed over the original finish without using a bonding agent and the whole thing has blown.
Either way, if the now "cleared ceiling" is sound, sort out any bad bits, tape over any cracks, then pva and replaster. I'd use a coat of bonding first then multi.