The following article is an edited transcript based on the David Turnbull Lecture given by Frank S. Bates of the University of Minnesota on December 1, 2004, at the Materials Research Society Fall Meeting in Boston. Bates received the award for “pioneering contributions to the fundamental understanding of structure and properties of complex polymeric materials, particularly block copolymers and polymeric vesicles, coupled with outstanding lecturing, writing, teaching, and educational leadership.” This article outlines the research accomplishments of a group of Bates' students that provide fresh insights into the molecular factors governing complex self-assembly in block copolymers. Three triply periodic and multicontinuous network phases were discovered in poly(isoprene-bstyrene-b-ethylene oxide) (ISO) triblock copolymers.Two cubic phases (Q230 and Q214) and an orthorhombic phase (O70) were identified using small-angle x-ray scattering (SAXS), transmission electron microscopy (TEM), birefringence measurements, and dynamic mechanical spectroscopy, along with level-set modeling. These findings establish a concrete strategy for locating potentially valuable network morphologies in ABC triblock copolymer melts.