Polyelectrolytes are polymers carrying either positively or negatively charged ionizable groups. Because of the presence of charged groups, the properties of these polymers are strongly influenced by the electrostatic interactions. The properties of these polymers in solutions and at charged surfaces depend on the fraction of dissociated ionic groups, solvent quality for polymer backbone, solution dielectric constant, salt concentration, and polymer-substrate interactions, etc. The goal of our research is to investigate and elucidate the nature of polyelectrolytes by either atomistic or coarse-grained model. The first stage of our research is the atomistic molecular dynamics simulations to study the conformational properties of polyelectrolyte chains, the phenomenon of counter-ion condensation, dynamics of polyelectrolyte solutions, etc. The results of atomistic simulations provide references for the development of coarse-grained model. In the next stage, we develop systematically coarse-grained models, in which we take into account the local chemical detail (bond angle and torsional angle distributions, arrangement of charged groups), as well as the effect of the solvent. Simulations with such detail can provide insight not available from generic lattice or bead-spring models. The applicability of the coarse-grained models is not limited to polymers, which can be extended to biological systems such as DNA and membrane.