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The piping systems must fulfill the criteria of hydraulic efficiency and structural durability, particularly for elbow pipes that experience sudden direction changes resulting in secondary flows, pressure drop, and erosion risks. This paper provides a critical review of elbow geometry modifications to address the issue of pressure drop and erosion risks while placing them within a broader context of geometric flow stabilization principles. The paper not only provides an overview of curvature ratio (R/D), cross-sectional changes, connecting lengths, and modified elbow geometry configurations but also makes an attempt to link internal pipe flow behavior with the principles of aerodynamic flow stabilization used in crosswind shielding and flow control systems. In addition to this, a critical methodology discussion is provided by comparing conventional Reynolds-Averaged Navier-Stokes (RANS) equations with new trends and techniques such as the Lattice Boltzmann Method (LBM) used for simulating complex vortex flows and unsteady flow behaviors. The paper further emphasizes the need to move away from traditional single-parameter geometric modifications towards multi-objective optimization techniques that incorporate multiple constraints related to pressure drop, erosion rates, structural integrity, and manufacturability constraints. The results show that the optimization of the curvature ratios and connecting lengths of the pipes effectively reduces erosion and stabilizes the gradients, although methodological inconsistencies in the approach to turbulence modeling and validation persist. This review article synthesizes the current knowledge and introduces an integrated approach for future research and elbow pipe design.