Exciting new developments in polyolefin synthesis give rise to olefinic block copolymers with properties typical of thermoplastic elastomers. The blocky copolymers synthesized by chain shuttling technology consist of crystallizable ethylene-octene blocks with low comonomer content and high melting temperature (hard blocks), alternating with amorphous ethylene-octene blocks with high comonomer content and low glass transition temperature (soft blocks). This paper describes the materials science of these unique polymers as characterized by thermal analysis, X-ray diffraction, microscopy, and tensile deformation. The crystallizable nature of the hard block and the crystalline morphologies are consistent with an average hard block length that is well in excess of 200 carbon atoms. The crystallizable blocks are long enough to form well-organized lamellar crystals with the orthorhombic unit cell and high melting temperature. The lamellae are organized into space-filling spherulites in all compositions even in copolymers with only 18 wt % hard block. The morphology is consistent with crystallization from a miscible melt. Crystallization of the hard blocks forces segregation of the noncrystallizable soft blocks into the interlamellar regions. Good separation of hard and soft blocks in the solid state is confirmed by distinct and separate beta- and alpha-relaxations in all the blocky copolymers. Compared to statistical ethylene-octene copolymers, the blocky architecture imparts a substantially higher crystallization temperature, a higher melting temperature and a better organized crystalline morphology, while maintaining a lower glass transition temperature. The differences between blocky and statistical copolymers become progressively more apparent as the total comonomer content increases.