The present invention provides curable and cured propylene-based elastomers, optionally including a diene, and having isotactic polypropylene crystallinity, a melting point by DSC equal to or less than 110° C., and a heat of fusion of from 5 J/g to 50 J/g. The present invention also provides blend compositions comprising any of the propylene-based elastomers described herein. The present invention also provides compositions comprising any of the propylene-based elastomers described herein and 1 to 100 parts by weight of inorganic filler per 100 parts of polymer. The present invention also provides films, fibers, fabrics, molded objects, and extruded forms which include any of the inventive compositions described herein.