Fluoride and oxide perovskite structures are attracting huge interest in recent years due to their special functionalities. In this thesis, the theoretical investigation on wide range of useful compounds from perovskite family have been studied thoroughly for their possible technological applications. Within the framework of Density Functional Theory (DFT), structural, elastic, mechanical, electronic, optical, magnetic and thermodynamic properties are studied by employing Full Potential-Linearized Augmented Plane Wave (FP-LAPW) method. For the said investigation, the WIEN2k package is utilized. The investigations on fluorine based strontium series of perovskites SrMF3 (M = Li, Na, K, Rb) reveals that in these mechanically stable fluoroperovskites, brittleness and ionic behavior are dominated which decreases from SrLiF3 to SrRbF3. Calculated energy band profiles confirm wide and direct (Γ-Γ) bandgap. A predominant characteristic associated with cation replacement shows that Li by Na, Na by K, and K by Rb significantly reduces the direct bandgap in SrMF3 (M = Li, Na, K, Rb) compounds. This crucial variation is responsible for working in different Ultra-Violet regions of the spectrum. Furthermore, from application point of view, they could preferably be used in lens materials because they would not tolerate birefringence that would make design of lenses difficult but also can be used in the confinement of light for Light Emitting Devices. The optimizations of structural parameters for rubidium based fluoroperovskite, RbHgF3 is done with variety of approximations, which validates through comparison with available experimental data. Energy band profile authenticates that inspected material is a narrow and indirect energy bandgap (M–Γ) semiconductor while contour maps of electron density verifies, mixed covalent-ionic behavior. In addition to it, optical responses show wide range of absorption and reflection in high frequency regions. Several elastic and mechanical parameters, reveals that protactinium based oxide series of perovskites XPaO3 (X = K, Rb) are mechanically stable and possesses weak resistance to shear deformation as compared with resistance to unidirectional compression while flexible and covalent behaviors are dominated in them. The analysis of band profile through Tran–Blaha modified Becke–Johnson (TB-mBJ) potential highlights the underestimation of bandgap with traditional Density Functional Theory (DFT) approximation. Specific contribution of electronic states are investigated by means of total and partial density of states and it can be evaluated that both compounds are direct bandgap (Γ–Γ) semiconductors. The study on BaMO3 (M= Pa,U) explores, type of chemical bonding with the help of variations in electron density difference distribution that is induced due to changes of second cation. The results of electronic properties illustrate direct bandgap (Γ-Γ) semi-conductive nature with the bandgap of 4.20 eV and 4.01 eV for BaPaO3 and BaUO3 compounds respectively. The band gap dependent optical properties such as complex dielectric function Ԑ (ω), optical conductivity σ (ω), refractive index n (ω), reflectivity R (ω), and effective number of electrons (neff) via sum rules are reported for the first time.The investigations on KXF3 (X = V, Fe, Co, Ni) authenticates that this class of fluoroperovskites are elastically as well as mechanically stable and anisotropic while KCoF3 is harder than rest of the compounds. The calculated spin dependent magnetoelectronic properties in these compounds shows that exchange splitting is dominated by N-3d orbital. The stable magnetic phase optimizations verify the experimental observations at low temperature. The present methodology represents an influential approach to calculate the whole set of mechanical and magneto-opto-electronic parameters, which would support to understand various physical phenomena and empower device engineers for implementing these materials in spintronic applications.The pressure induced structural, elastic, mechanical, electronic, optical and thermodynamic properties of SrLiF3, SrNaF3, SrKF3, SrRbF3, and CaLiF3 are computationally calculated for their possible technological outcomes. All elastic and mechanical parameters are linearly dependent on applied pressure and an increase in pressure improves tensile strength and stiffness, on the other hand, reduces brittleness and compressibility of these cubic fluoroperovskites. It is observed that an increase in pressure considerably improves the wide and direct (Γ-Γ) electronic bandgap. The optical parameters of SrLiF3 and SrNaF3 shows that all optical responses shift towards higher energy ranges which divulges that both are more suitable for optoelectronic devices at higher pressure ranges. Consequently, our theoretical work has been benchmarked various quantum mechanical effects, which will motivate research scholars to done theoretical as well as experimental investigations on fluoride and oxide perovskites that must be considered to understand and utilize these materials in fabricating practical devices for optoelectronic, microelectronic, spintronic and piezoelectric applications.