Charged polymers exhibit interesting and complex structures, functions, and dynamics in both natural and synthetic environments. The equilibrium and dynamic properties of charged polymers are determined by the interplay of entropy and enthalpy from electrostatic interactions between charged polymers, counterions, salt ions, and short-ranged Van der Waals interactions. This work is mostly focused on understanding the equilibrium and dynamic behaviors of charged polymers in different environments. We use computer modeling, mostly coarse-grained Langevin dynamics simulations, to simulate complex environments having charged polymers, solvents, and charged ions. Our topics of interest in this work include a comparison of electrostatic potential across a nanopore using atomistic and coarse-grained approaches, unfolding of RNA hairpins in response to applied external forces, chain conformation of a tagged polyelectrolyte chain inside a polyelectrolyte complex, and effects of charge density, temperature and salt concentration on the aggregated structure of oppositely charged polymers in semi-dilute solutions.\\ We model the electrostatic potential across charge decorated $\alpha$-Hemolysin protein nanopores using both all-atom molecular dynamics simulations and coarse-grained Langevin dynamics simulations. We observe that the coarse-grained method gives a good approximation of the atomistic approach. We also model simple RNA hairpin architectures and a nanopore using coarse-grained method. We monitor the mechanism of unfolding when different RNA hairpin architectures of an equal number of nucleotides are passing through a nanopore under the application of an electric field. We find that the RNA with longer hairpins requires more force to unfold and translocate through the nanopore. We also observe a distinct signature of unfolding time for the bases before and after unpaired bases in the RNA hairpin models. Next, by using coarse-grained Langevin dynamics simulations of polyelectrolytes of symmetric and flexible polyelectrolytes of opposite charges alongside explicit counterions and salt ions, we study the role of charge density, polymer concentration, temperature, and salt concentration on the structure and dynamics of complexes. In a system of highly charged polyelectrolytes, the average radius of gyration ($\langle R_g \rangle$) of a labeled chain and the size-scaling exponent $\nu$ of a single isolated chain are maximum, and they shrink when two charged polymers of opposite charges come together forming a complex. The $\langle R_g \rangle$ of a labeled chain inside a polyelectrolyte complex increases with increasing the size of the complex reaches a plateau once the reasonable size of the complex is formed. The value of $\nu$ also increases and reaches a plateau of $0.5$, indicating that the labeled chain inside the complex shows Gaussian-like statistics. We observed that in semi-dilute solutions of polyelectrolyte complexes, the formation of complex structures is enhanced with an increase in charge density of polymers and with a decrease in temperature. The aggregates are de-complexed with an increase in salt concentration. We also observed that in the semi-dilute regime $\langle R_g \rangle$ and $\nu$ of a labeled chain is independent of the size of the complex formed, the charge density of the polymer, temperature, and salt concentration and chains show Gaussian-like conformations. Further, we observed that an isolated polyelectrolyte chain shows diffusive behavior, but the labeled chain in the complexes follows non-diffusive dynamical law as the chain becomes a part of the physical network due to the presence of other chains in the complex. The results of these studies complement experimental studies and provide a more in-depth understanding of already observed phenomena.