Li-ions are charged in Constant Current mode from cutoff voltage(2.75V-3.2V) until maximum voltage(4.2-4.3V), and charged some more in Constant Voltage mode until cutoff current(<0.1C) is reached. Nominal voltage is in the middle at 3.7V.

I believe these (cutoff voltage, CC->CV switch, cutoff current point) are commonly referred to as (0%, 80%, 100%) levels respectively, if safety margins and psychological tweaks are not considered.

Which leads to an assumption that it is this Constant Voltage region that is often said to be damaging to cells, though I don’t know exactly why.

Neither 0% nor 100% are dangerous, but lithium ion batteries wear out a lot faster if you cycle them all the way instead of only staying within 20-80%.