In this thesis, we investigate some important aspects of general relativity in the framework of Chern-Simons modified gravity. We focus on some dark energy models, gravitational collapse, cosmological analysis of FRW metric and consistency of the solutions. Firstly, we discuss four different dark energy models, for example, Ricci dark energy model, holographic dark energy model with Granda-Oliveros cut-off, modified holographic Ricci dark energy model and another model having higher order derivative term of the Hubble parameter by finding their scale factors and density parameters. Further, holographic dark energy model and modified holographic Ricci dark energy model are explored and the correspondence between quintessence, K-essence, tachyon and dilaton models. Secondly, we discuss gravitational collapse in the context of CS gravity by finding apparent and cosmological horizons, naked singularities, black holes and the effect of Newtonian force on the gravitational collapse. Next, we discuss the cosmological analysis of FRW universe by taking different combinations of matter, radiation and cosmological term with CS term in the dynamical background of Chern-Simons modified gravity. For all these combinations, we explore density, deceleration parameter, equation of state and stability analysis with the graphical interpretation. At the end, we find the consistency of well-known static G¨odel type solution in the context of non-dynamical Chern-Simons modified gravity and non-static spherically symmetric solutions in the presence of cosmological constant in the framework dynamical Chern-Simons modified gravity.