Polymer flooding is a proven chemical Enhanced Oil Recovery (cEOR) method that boosts oil production beyond waterflooding. Thorough theoretical and practical knowledge has been obtained for this technique through numerous experimental, simulation, and field works. According to the conventional belief, this technique improves macroscopic sweep efficiency due to high polymer viscosity by producing moveable oil that remains unswept after secondary recovery. However, recent studies show that in addition to viscosity, polymer viscoelasticity can be effectively utilized to increase oil recovery by mobilizing residual oil and improving microscopic displacement efficiency in addition to macroscopic sweep efficiency. The polymer flooding is frequently implemented in sandstones with limited application in carbonates. This limitation is associated with extreme reservoir conditions, such as high concentrations of monovalent and divalent ions in the formation brine and ultimate reservoir temperatures. Other complications include the high heterogeneity of tight carbonates and their mixed-to-oil wettability. To overcome the challenges related to severe reservoir conditions, novel polymers have been introduced. These new polymers have unique monomers protecting them from chemical and thermal degradations. Monomers, such as NVP (N-vinylpyrrolidone) and ATBS (2-acrylamido-2-methylpropane sulfonic acid), enhance the chemical resistance of polymers against hydrolysis, mitigating the risk of viscosity reduction or precipitation in challenging reservoir conditions. However, the viscoelasticity of these novel polymers and their corresponding impact on microscopic displacement efficiency are not well established and require further investigation in this area. In this study, we comprehensively review recent works on viscoelastic polymer flow under various reservoir conditions, including carbonates and sandstones. In addition, the paper defines various mechanisms underlying incremental oil recovery by viscoelastic polymers and extensively describes the means of controlling and improving their viscoelasticity. Furthermore, the polymer screening studies for harsh reservoir conditions are also included. Finally, the impact of viscoelastic synthetic polymers on oil mobilization, the difficulties faced during this cEOR process, and the list of field applications in carbonates and sandstones can also be found in our work. This paper may serve as a guide for commencing or performing laboratory- and field-scale projects related to viscoelastic polymer flooding.