Translucent propylene-based elastomeric compositions

mfA composition is described in one aspect as comprising one or more propylene-α-olefin terpolymers; wherein the propylene-α-olefin terpolymer(s) possess a melting temperature (T) within the range of from less than 105° C., and a heat of fusion (H) within the range of from less than 75 J/g; one or more polyolefin(s); and oil; wherein fillers are present, if at all, at a level that maintains a Haze value of 65% or less for the composition. The terpolymer in one embodiment is a polymer comprising at least 65 wt %, by weight of the terpolymer, of propylene-derived units, within the range of from 5 to 35 wt % of ethylene or other α-olefin and a diene such as ethylidiene norbornene, and in certain embodiments having a Mooney Viscosity (ML(1+4)@125° C.) within the range of from 10 to 50 (ASTM D1646). The compositions can be cured to form transparent or translucent articles such as sheets that are also flexible.