Provided are crosslinkable propylene-based copolymers, methods for making the same, elastomeric compositions including the same, and articles made therefrom, e.g., films and fibers. Exemplary elastomeric compositions are composed of at least one propylene-based polymer comprising propylene derived units and one or more dienes, the propylene-based polymer having a triad tacticity of from 50% to 99% and a heat of fusion of less than 80 J/g; about 0.5 wt % to about 10 wt % vinyl siloxane; and about 0.1 wt % to about 1.0 wt % peroxide. The elastomeric compositions can be extruded and crosslinked at a temperature of at least about 50° C. and a relative humidity of at least about 90% to provide a crosslinked elastomeric composition. The crosslinked elastomeric compositions are particularly useful for making fibers and films.