In this thesis, we study various evolutionary aspects of relativistic collapsing systems, thin-shell wormholes as well as cosmos by incorporating the e®ects of di®erent physical parameters. We consider both spherical and cylindrical stellar objects ¯lled with electromagnetic °uids and discuss their dynamical instability under radial oscillations. The dynamical instability of homogeneous sphere as well as relativistic polytropes is discussed by taking di®erent values of charge in Newtonian and post Newtonian regimes. Moreover, we evaluate the ranges of radii as well as adiabatic index for both charged and uncharged dissipative homogeneous cylinder. It is noted that dynamical instability occurs in the presence of charge if the gaseous mass contracts to the limiting radius. We discuss stability of thin-shell wormholes coupled with nonlinear electrodynam- ics in the vicinity of di®erent cosmological models for exotic matter. A general equa- tion of state is considered in the form of linear perturbation which explores stability of the respective wormhole solutions. We assume linear, logarithmic and Chaplygin gas models to study exotic matter at thin-shell and evaluate maximum viable regions for stability with di®erent values of the involved parameters. We also study stability of thin-shell wormholes in Einstein Ho®mann-Born-Infeld electrodynamics following the same dynamical approach. It is found that the Ho®mann-Born-Infeld parameter and electric charge enhance the stability regions. Finally, we discuss dynamical stability of isotropic and homogenous universe model via phase space analysis by taking a noninteracting mixture of electromagnetic and viscous radiating °uids whose viscous pressure satis¯es a nonlinear version of the Israel-Stewart transport equation. We evaluate corresponding critical points for var- ious choices of physical parameters. It is found that bulk viscosity as well as elec- tromagnetic ¯eld enhances the stability of accelerated expansion of the isotropic and homogeneous cosmos. We also study phase space analysis of locally rotationally sym- metric Bianchi type I universe model by taking di®erent linear combinations for the interactions between scalar ¯eld models and dark matter. This indicates a matter dominated epoch ultimately followed by a late accelerated expansion phase. We con- clude that all the critical points lead to accelerated expansion of the universe for tachyon coupled ¯eld.