Polyelectrolytes are polymers that develop substantial charge when dissolved or swollen in a highly polar solvent medium such as water. The attendant electrostatic interactions — within a single polyelectrolyte, between polyelectrolytes, or with molecules/surfaces — produce physical properties much different than those for neutral polymers. Most polyelectrolyte solution and gel properties vary sharply with addition of simple electrolytes, which screen electrostatic interactions according to concentration. Scientists are just beginning to understand polyelectrolyte electrostatic interactions, which are known to play an important role in the natural world. Important concepts for polyelectrolytes are counterion condensation, electrostatic persistence length, electrostatic excluded volume, and Donnan equilibrium. Properties such as low angle scattered intensity, solution viscosity, osmotic pressure, polyelectrolyte and counterion diffusion coefficients, conductivity, adsorption, complexation, electric and magnetic birefringence, electrophoresis, titration, and gel swelling can only be understood by accounting properly for electrostatic interactions. These distinctive properties underlie applications in colloid stabilization, surface modification, rheology control, and controlled release.