This thesis is devoted to explore some cosmological implications in gravity and generalizedgravity. Initially, we discuss the cosmological reconstruction of theory (where,and represent the Ricci scalar, scalar invariant and scalar field) corresponding to power law and de Sitter evolution in the framework of FRW universe model. We derive the energy conditions for this modified theory which seem to be more general and can be reduced to some known forms of these conditions in general relativity,andtheories. We also present the general constraints in terms of recent values of snap, jerk, deceleration and Hubble parameters. The energy bounds are analyzed for reconstructed as well as known models in this theory. Finally, the free parameters are analyzed comprehensively. First and second laws of black hole thermodynamics are examined at the apparent horizon of FRW spacetime in gravity. In this modified theory, Friedmann equations are formulated for any spatial curvature. These equations can be presented into the form of first law of thermodynamics for ̂̂ , wherêis an extra entropy term because of the non-equilibrium presentation of the equations and ̂ for the equilibrium presentation. The generalized second law of thermodynamics (GSLT) is expressed in an inclusive form where these results can be represented in GR,andgravities. Finally to check the validity of GSLT, we take some particular models and produce constraints of the parameters. Moreover, we examine static spherically symmetric wormhole solutions in generalizedgravity. To do this, we consider three different kinds of fluids: anisotropic, barotropic and isotropic. We explore differentmodels and inspect the energy conditions for all of those three fluids. It is found that under some models in this theory, it is possible to obtain wormhole solutions without requiring exotic matter. From our results, one can conclude that for all three cases of fluids stable and realistic wormhole solutions can be constructed.Further, we have consideredaction which is non-minimally coupled to the xi scalar field. In this context, we obtain the exact analytical solutions for inflationary era as well as find a graceful exit condition from inflation. We calculate the perturbed parameters, i.e., number of e-folds, slow-roll parameters, scalar and tensor power spectra, corresponding spectral indices and ultimately tensor to scalar ratio. It is showed that the power spectra lead to blue-tilt for this model. The trajectories of the perturbed parameters are plotted to compare the results with recent observations.Finally, we will discuss cosmological models using Bianchi type I for anisotropic fluid intheory of gravity which involves scalar potential. For this purpose, we consider power law assumptions of coupling function and scalar field along with the proportionality condition of expansion and shear scalars. We choose twomodels and obtain exact solutions of field equations in both cases. For these constructed models, the behavior of different physical quantities like EoS parameter, self-interacting potential as well as deceleration and skewness parameters is explored and illustrated graphically for the feasible ranges of free parameters. It is concluded that anisotropic fluid approaches to isotropy in later cosmic times for both models which is compatible with the observational data.