Polymers are prototypical examples of soft-matter systems. The talk will first focus on equilibrium statistical mechanics, and introduce basic concepts like the random walk and the self-avoiding walk. This is complemented by a discussion of the notion of coarse-graining and scale invariance, which is at the basis of modeling polymers in terms of simple bead-spring models. The second part will then discuss the basics of polymer dynamics, in terms of the fundamental Rouse, Zimm, and reptation models. The third part is devoted to a brief overview over Monte Carlo and Molecular Dynamics models and simulation algorithms, which are directly based upon the insight into the essential physics. If time permits, a brief outlook on the physics of membranes will be added.