The challenges and opportunities in studying the theoretical concepts and techniques of polymer science are presented. The concepts of statistical mechanics and condensed-matter physics are the foundations of the polymer science studies and thermodynamic, structural, and dynamic properties of polymer solutions, melts, and solids. Polymer science, biopolymers, and polyelectrolytes find applications in polymer physics, biology, and biotechnology. DNA looping in a lac repressor in Escherichia coli is used to illustrate polymer science studies for a real biological problem. Polymer theory is also applied for polymer theory in semiconducting polymers and organic optoelectrical materials. The semiconducting polymers combine the optical and electronic properties of semiconductors with the mechanical properties of polymers. The polymer science can assess casting-solvent quality, blend composition, and morphology of semiconducting polymers.