Polymer molecules containing chemically dissimilar segments have been investigated for many years. Their synthesis and characterization are challenging, and it is evident that their properties are often unusual and useful as witnessed by several books and reviews published on block and graft polymers. In this article we intend to review parts of this rapidly expanding area of polymer research of particular interest in rubber chemistry and technology, namely linear elastomeric block polymers. Sometimes the literature specifies the elastomeric nature of the products, on other occasions it does not. We have arbitrarily included those monomer combinations in which at least one monomer is known to form rubbery homopolymer. Urethan elastomers have been excluded because they have been extensively described elsewhere. In the broadest sense, block polymers are molecules in which two or more chemically dissimilar segments are joined end to end, a feature which distinguishes them from graft polymers. Each segment or block is usually a long sequence of units of a single monomer (A or B or C, etc.), but it may also be a long sequence of randomly copolymerized units (A plus B or C, etc.). Both types are known.