  Any first course on polymer physics teaches that the dynamics of a tagged
monomer of a polymer is anomalously subdiffusive, i.e., the mean-square
displacement of a tagged monomer increases as $t^\alpha$ for some $\alpha<1$
until the terminal relaxation time $\tau$ of the polymer. Beyond time $\tau$
the motion of the tagged monomer becomes diffusive. Classical examples of
anomalous dynamics in polymer physics are single polymeric systems, such as
phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation,
translocation through a narrow pore in a membrane, and many-polymeric systems
such as polymer melts. In this pedagogical paper I report that all these
instances of anomalous dynamics in polymeric systems are robustly characterized
by power-law memory kernels within a {\it unified} Generalized Langevin
Equation (GLE) scheme, and therefore, are non-Markovian. The exponents of the
power-law memory kernels are related to the relaxation response of the polymers
to local strains, and are derived from the equilibrium statistical physics of
polymers. The anomalous dynamics of a tagged monomer of a polymer in these
systems is then reproduced from the power-law memory kernels of the GLE via the
fluctuation-dissipation theorem (FDT). Using this GLE formulation I further
show that the characteristics of the drifts caused by a (weak) applied field on
these polymeric systems are also obtained from the corresponding memory
kernels.
