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.degree. C., a heat of fusion of from 5 J/g to 50 J/g, an ultimate tensile strength of 1 MPa or greater, a Die C tear strength of 50 lb/in or greater, and a ratio of Shore A hardness to MFR@230.degree. C. prior to crosslinking of 160 or less, and comprising at least 75 wt % propylene-derived units, at least 5 wt % ethylene-derived units, and from 0.3 to 10 wt % diene-derived units. The present invention also provides elastomeric compositions comprising a crosslinked propylene-based elastomer as described herein and from 0 to 5 parts by weight of carbon black per 100 parts of polymer. The present invention also provides articles such as films, fibers, nonwovens, molded objects, and extruded forms which include any of the inventive compositions described herein.