Understanding the reason behind the observed accelerating expansion of the Universe is one of the most notable puzzles in modern cosmology, and conceivably in fundamental physics. In the upcoming years, near-future surveys will probe structure formation with unprecedented precision and will put firm constraints on the cosmological parameters, including those that describe properties of dark energy. In light of this, in this thesis, we mainly focus on characterizing the non-linear evolution of dark energy and modified gravity models with the aim to probe some of these models precisely while treating all cosmological components including the dark energy part accurately. This treatment of the dark sector is especially required by the future high precision cosmological surveys.