Stereoblock polypropylenes are complicated, intriguing, and challenging polymers. It may be worthy to open this chapter by recalling that, according to the IUPAC Glossary of Basic Terms in Polymer Science,1 a block is “a portion of a macromolecule comprising many constitutional units, that has at least one feature which is not present in the adjacent portions”; a block macromolecule is “a macromolecule which is composed of blocks in linear sequence”; a stereoblock macromolecule is “a block macromolecule composed of stereoregular, and possibly non-stereoregular, blocks.” On paper, applying these definitions to propylene polymers is straightforward with the notable exception of the “stereoblock-isotactic” case, which will be discussed specifically in the last part of this section. On the other hand, demonstrating that these structures exist for a real polypropylene sample is a formidable microstructural problem; in fact, of the many cases claimed in the scientific and patent literature, those rigorously proven to be stereoblock polypropylenes can be counted on the fingers of one hand.