Thermoelectric (TE) materials have lately attracted a lot of attention and sparked a flurry of research because of their potential for energy conversion and broad spectrum of applications, including waste heat recovery, thermocouples, sensors, and refrigeration. Additionally, they could potentially be able to offer extremely effective and eco-friendly methods for energy production and harvesting, which might aid in addressing the world's energy concerns. Concerning the advancement in condensed matter physics, although a plethora of research has been devoted to identifying suitable TE materials over the years, there is still scope for the exploration of new materials. This review article strives to project extensive progress in the field of thermoelectricity, commencing with a discussion on various classes of TE materials scrutinized based on TE coefficients such as thermopower, power factor, and thermal conductivity computed within the framework of DFT, combined with an in-depth look at the computational techniques used. A wide range of prospective TE material classes, including chalcogenides, pnictides, oxides, perovskites, transition metal dichalcogenides (TMD), and a few more, are meticulously addressed, stressing the unique characteristics of each class in separate sections and subsections. SrAgChF (Ch = S, Se, Te), with its superlattice structure, boasts high thermopower for both carriers, making it ideal for power generation. Similarly, ThOCh (Ch = S, Se, Te) and NbX2Y2 (X = S, Se, Y = Cl, Br, I) chalcogen materials exhibit significant thermoelectric properties in both bulk and monolayer forms. Fe2GeCh4 (Ch = S, Se, Te) demonstrates exceptional anisotropic TE characteristics, advantageous for device applications. Structurally resembling chalcopyrites, Zn-based pnictides show high efficiency, validated by the analysis of power factor scaled by temperature and relaxation time (S2σT/τ: where S is thermopower, σ is electrical conductivity, S2σ is power factor, T is temperature and τ is the relaxation time). Moreover, CaLiPn (Pn = As, Sb, Bi) emerges as more favorable for TE applications than SrLiAs, displaying low lattice thermal conductivity. Among transition metal dichalcogenides (TMDs), OsX2 (S, Se, Te) exhibits high thermopower, while FeS2 displays remarkable thermoelectric properties in both marcasite and pyrite structural phases. In exploring 2D materials akin to graphene, ReS2's TE properties have been scrutinized across various forms, showcasing significant potential, especially when tailored for flexibility. Compounds like CaSrX (X = Si, Ge, Sn, Pb) and ZnGeSb2 exhibit notable TE features, indicating avenues for strain-engineered modulation of TE properties. Lattice dynamics play a pivotal role in TE efficiency, driving investigations into phonon dispersion and thermal properties across materials. CsAgO's remarkably low lattice thermal conductivity highlights its promise as a TE material. Despite the effectiveness of semiclassical approximations, accurately predicting transport parameters requires accounting for scattering effects. Incorporating such factors is essential for precise estimation of the thermoelectric figure of merit (ZT). Notably, CsAgO's low lattice thermal conductivity contributes to its effectiveness, boasting a ZT exceeding 1.4. Layered compounds like CuTlX (X = S, Se) exhibit extreme anisotropy in lattice thermal conductivity and achieve ZT values surpassing one at 300 K. LaAgXO (X = Se, Te) shows a high ZT exceeding 2.5, particularly under heavy carrier doping. The best aspects of the compounds studied, the future of TE materials in the context of device application, the development of flexible and wearable TE materials, and strategies for improving TE parameters are all discussed in this review's conclusion.