In this thesis, collapsing models have been studied in different theories of gravitation. In particular, we have explored the Phenomenon of collapse in general theory of relativity, f(R) theory and f(R,G) theory. Firstly, we discuss the collapsing models in the framework of general theory of relativity. The collapsing model of charged anisotropic fluid with positive cosmological constant in four dimensions is addressed. It is noted that in the presence of electromagnetic field the collapsing rate is faster. When the fluid remains anisotropic and the electric field strength E0(t,r) vanishes, our investigations are in full agreement with the results obtained by Ahmad and Malik [59]. We also address five dimensional collapsing model with anisotropic pressure and positive cosmological constant and found exact analytic solutions to the field equations. We found that the area of cosmological horizon and black hole horizon has larger area in five dimensions than four dimensions. The shear-free gravitational collapse with heat flux is discussed by considering higher dimensional spherically symmetric spacetime as interior metric and higher dimensional Vaidya spacetime as exterior metric. The effects of dissipation on collapse are investigated. A simple approximate higher dimensional conformally flat model is proposed that satisfies the junction conditions. Temperature profile of the proposed model is also calculated. It is concluded that dissipation decreases the collapsing rate and temperature profile of the suggested model. We investigate higher dimensional spherically symmetric anisotropic collapsing solutions of the field equations, and to check the effects of higher dimensions on the density and pressures profile of the collapsing fluid. We have also studied the effects of higher dimensions on the dimensionless measure of an isotropy. Secondly, we study gravitational collapse of a perfect fluid in f(R) theory. We have solved the field equations by assuming linear equation of state (p = ωµ) with ω = −1. We have also discussed formation of apparent horizon and singularity. It is shown that singularity does not depend on the radial coordinate r, and is thus non central, that is, it can take place at all points simultaneously. The dynamics of spherical perfect fluid collapsing model with heat flux is investigated in f(R,G) gravity. For this purpose, we adopt the MisnerSharp formalism to construct the dynamical equations and drive transport equation. Furthermore, we examine the collapsing rate by coupling the transport and dynamical equations. It is noted that for constant f(R,G) model the collapsing rate reduces.