In this thesis we focused on explaining the critical behaviour and phase transition in black holes with the variation of cosmological constant. The simplest choice is Schwarzschild black hole which is locally thermodynamically unstable. In the presence of charge and angular momentum there is a phase transition from unstable to stable branch in the system of black holes. So the thermodynamics quantities such as charge and angular momentum make the system more stable. Also there is a phase transition from unstable to stable phase in Schwarzschild-Anti de Sitter (AdS) black hole with the cosmological constant ? as thermodynamic pressure. We consider the critical behaviour and phase transition of charged black hole (Reier-Nordstrom) and rotating black hole (Kerr) in AdS space time. A conjugate quantity to the thermodynamic pressure ? is the thermodynamic volume which can formally be obtained from the first law of black hole thermodynamics. In this condition, the critical behaviour and critical exponent Reier-Nordstrom-AdS and Kerr-AdS are similar to Van der Waals fluid. We specifically study the thermodynamics of higher-dimensional rotating asymptotically flat and AdS black holes with the cosmological constant ? as thermodynamic pressure. We plot the associated thermodynamic potential (the Gi free energy) and study its behaviour to uncover possible thermodynamic phase transitions for both cases of single and multiply rotating parameter. The results show that the single spinning Kerr-AdS has a reentrant phase transitions of multicomponent liquids and multiply-rotating Kerr-AdS black holes exhibit a rich set of interesting thermodynamic phenomena analogous to the `every day thermodynamics' of simple substances, multiple first-order solid/liquid/gas phase transitions of the Van der Waals type. Furthermore, critical behaviour and phase transition of hairy black holes in massive gravity and black holes in higher order gravities are considered. We study Gauss Bonnet-Born Infeld-AdS black holes (GB-BI-AdS) and Born-Infeld-AdS (BI-AdS) black holes in the third order of Lovelock gravity. We find "reentrant and triple point phase transitions" (RPT-TP) and also "multiple reentrant phase transitions" (multiple RPT) as the pressure of the system increased. Also the critical behavior and phase transition of Myers-Perry black holes with equal angular momenta by including the corrections beyond the semi classical approximation on Hawking temperature in the grand canonical ensemble are investigated. There are several different methods for calculating the corrections to the semi classical Bekenstein-Hawking entropy. These are based on statistical mechanical arguments, field theory methods, quantum geometry, the Cardy formula, the generalized uncertainty principle, etc. Finally, the future singularities of the universe by using the Friedmann equations with the effect of both the Entropic force and running gravitational coupling is calculated. The effect of entropic force changes the pressure and energy density behaviours at singularity time in the singularity type II. But running gravitational coupling as function of energy density of the universe changes time evolution of the universe.