From the beginning
of life with the information-containing polymers
until the present era of a plethora of water-based materials in health
care industry and biotechnology, polyelectrolytes are ubiquitous with
a broad range of structural and functional properties. The main attribute
of polyelectrolyte solutions is that all molecules are strongly correlated
both topologically and electrostatically in their neutralizing background
of charged ions in highly polarizable solvent. These strong correlations
and the necessary use of numerous variables in experiments on polyelectrolytes
have presented immense challenges toward fundamental understanding
of the various behaviors of charged polymeric systems. This Perspective
presents the author’s subjective summary of several conceptual
advances and the remaining persistent challenges in the contexts of
charge and size of polymers, structures in homogeneous solutions,
thermodynamic instability and phase transitions, structural evolution
with oppositely charged polymers, dynamics in polyelectrolyte solutions,
kinetics of phase separation, mobility of charged macromolecules between
compartments, and implications to biological systems.