1. Introduction 2. Charged chains at infinite dilution - asymptotic properties 2.1 Definition of the model and Flory-like calculation 2.2 Variational approaches 2.3 Renormalization group calculations 2.4 Screening of electrostatic interactions 2.5 Annealed and quenched polyelectrolytes 3. Local aspects of screening 3.1 Counterion condensation 3.2 Poisson Boltzmann approach 3.3 Attractive electrostatic interactions 4. Electrostatic rigidity 4.1 The Odijk-Skolnick-Fixman theory 4.2 Alternative calculations for flexible chains 4.3 The case of poor solvents 5. Charged gels and brushes 5.1 Grafted polyelectrolyte layers 5.2 Polyelectrolyte gels 6. Semidilute solutions 6.1 Ordering transitions in polyelectrolyte solutions 6.2 Correlation length and osmotic pressure of semi-dilute polyelectrolyte solutions 6.3 Electrostatic rigidity in semidilute solutions 6.4 Concentrated solutions of flexible polyelectrolytes 6.5 Mesophase formation in poor solvents 7. Dynamical properties 7.1 Mobility and electrophoretic mobility of a single charged chain 7.2 Viscosity of polyelectrolyte solutions 8. Conclusions ; Comment: 81 pages, plain TEX. Figures available on request (barrat@dpm.univ-lyon1.fr). To appear in "Advances in Chemical Physics" (Prigogine, Rice Editors)