This chapter presents salient concepts to understand a vast literature on dynamics of charged macromolecules. Starting from a description of hydrodynamic interaction, dynamics of folded proteins, colloids, flexible polyelectrolytes, DNA are described. For flexible macromolecules, the models of Rouse, Zimm, reptation, and entropic barrier are developed in increasing order of complexity. Using this groundwork, the phenomena of ordinary-extraordinary transition, electrophoretic mobility, and topologically frustrated dynamical state are explained.

The dynamic evolution of a classic molecular system is first introduced formally via Liouville equation. Then, single-particle time correlation functions and their general properties (like short and long time limits) for orientational correlation functions (OCF) in liquid crystals are discussed and translational and orientational diffusion coefficients are introduced. The link between OCFs, obtainable from computer simulations, and experiments is established with Linear Response theory and examples from dielectric relaxation, ionic and thermal conductivity, viscosities are presented, with reference to the literature. The rotational diffusion equation in an anisotropic fluid, normally employed to analyze experiments is also introduced, with explicit expressions derived for Fluorescence Depolarization.