A process for the precise control of polymer molecular weight distribution (MWD) shape is developed. Temporal control of polymer chain initiation was achieved through the metered addition of discrete initiating species to controlled radical polymerizations and anionic polymerizations. Series of polymers can be prepared with the same molar mass and breadth but with vastly different MWD shapes. Using anionic polymerization, living polymers with skewed distribution functions can be chain extended to afford well-defined block copolymers with systematically deviating compositions of molecular weights. Rheological measurements reveal that the MWD shape has an important influence on the viscoelastic behavior of homopolymer melts such as viscosity and storage modulus. Dynamic mechanical analysis showed that the Young’s modulus of block copolymers can be tuned over a broad range by modifying the shape of the MWD in one block. Investigation of the phase behavior of block copolymers by transmission small-angle X-ray scattering and grazing-incidence small-angle X-ray scattering demonstrates that the distribution symmetry enables tuning of the thin film domain spacing and the boundaries of the bulk morphological phase diagram. Additionally, the development of a kinetic model for the predictive design of MWDs is explored.