Block polymers (BPs) derived from biomass (biobased) are necessary components of a sustainable future that relies minimally on petroleum-based plastics for applications ranging from thermoplastic elastomers and pressure-sensitive adhesives to blend compatibilizers. To facilitate their adoption, renewable BPs must be affordable, durable, processable, versatile, and reasonably benign. Their desirability further depends on the relative sustainability of the renewable resources and the methods employed in the monomer and polymer syntheses. Various strategies allow these BPs' characteristics to be tuned and enhanced for commercial applications, and many of these techniques also can be applied to manipulate the wide-ranging mechanical and thermal properties of biobased and self-assembling block polymers. From feedstock to application, this review article highlights promising renewable BPs, plus their material and assembly properties, in support of de novo design strategies that could revolutionize material sustainability.