Unique copolymers comprising propylene, ethylene and/or one or more unsaturated comonomers are characterized as having: at least one, preferably more than one, of the following properties: (i) ¹³C NMR peaks corresponding to a regio-error at about 14.6 and about 15.7 ppm, the peaks of about equal intensity, (ii) a B-value greater than about 1.4 when the comonomer content of the copolymer is at least about 3 wt %, (iii) a skewness index, S_ix, greater than about -1.20, (iv) a DSC curve with a T_me that remains essentially the same and a T_max that decreases as the amount of comonomer in the copolymer is increased, and (v) an X-ray diffraction pattern that reports more gamma-form crystals than a comparable copolymer prepared with a Ziegler-Natta catalyst. These polypropylene polymers are made using a nonmetallocene, metal-centered, heteroaryl ligand catalyst. These polymers can be blended with other polymers, and are useful in the manufacture of films, sheets, foams, fibers and molded articles.