The novel quantum phases of material emerging from the interplay between the crystal symmetry, spin and orbital degrees of freedom are described through band theories. The topological insulating phase of the material is one such quantum phases that exhibit a bulk bandgap but have protected conducting states on their edge or surface. In the present thesis, we examine the family of Halide perovskites as possible candidate for inducing the topological phase as they have the right crystal symmetry, appropriate covalent bonding and adequate spin-orbit coupling. Through density functional calculations and model Hamiltonians, we explore a normal insulator (NI) to topological insulator (TI) phase transition in centrosymmetric CsSnX3 (X= Cl, Br, I) with hydrostatic pressure and strain in three of its polymorphs, namely, cubic, tetragonal, and orthorhombic. While the cubic phase demonstrates the NI-TI phase transition with pressure, tensile and compressive strain condition, the tetragonal phase is capable of doing so through tensile strain. Owing to large bandgap, the orthorhombic phase is not a suitable candidate for inducing the TI phase. Some of the halide perovskites can break the inversion symmetry which gives rise to Rashba coupling. We show that in such cases, the phase transition is first order and the TI phase creates a rarely observed Dirac circle through interpenetration of two Dirac cones. Analysis of band topology through model Hamiltonian led to the conceptualization of topological influencers that measures the ability of a certain chemical bonding, in relative to others, towards establishing a TI phase.