In this talk, I will start with several topics of polymer theory in the theme of statistical mechanics: symmetry-breaking-induced order/rigidity; fluctuation effects; stochastic dynamics/thermodynamics; path integrals. Then, along with these themes, I will discuss several of our related works including global/local phase separation in bulk/finite systems; renormalized theory of critical fluctuations; exact path integrals; correlation functions and thermal Casimir forces for confined fluctuations.