The present invention provides a crosslinked propylene-based elastomer having an isotactic propylene triad tacticity of from 65 to 95%, a melting point by DSC equal to or less than 110~C, a heat of fusion of from 5 J/g to 50 J/g, and a haze% per 100 mil thickness of 95 or less, and comprising at least 75 wt%
propylene-derived units, at least 5 wt% ethylene-derived units, and optionally 10 wt% or less of dime-derived units. In an embodiment, the present invention is a blend of a continuous phase of the crosslinked propylene-based elastomer and a dispersed phase of a crystalline polymeric compound. The present invention also provides elastomeric compositions comprising a crosslinked propylene-based elastomer as described herein and 100 parts by weight or less of a pigment per 100 parts of polymer. The present invention also provides films, fibers, nonwovens, molded objects, and extruded forms which include any of the inventive compositions described herein.