Linear programming (LP) is a pillar in the field of optimization and decision-making with far-reaching applications in engineering, economics, logistics, and data science. Classical algorithms, particularly the Simplex algorithm and Interior-Point methods, have been used to solve LP problems with great success. Nevertheless, the growing complexity and size of modern applications have brought into focus the shortcomings of these traditional methods, including high computational expense, problem-size sensitivity, and difficulties associated with degeneracy. This review article explores the development and improvement of traditional LP algorithms, specifically design modifications for better computational efficiency, scalability, and robustness. Some of the major developments addressed include algorithmic enhancements such as the Revised Simplex Method, incorporation of decomposition methodologies such as Dantzig–Wolfe decomposition, and inclusion of parallel computing paradigms. The article also discusses the development of hybrid algorithms that merge the principles of traditional methods with contemporary computational techniques to solve large-scale and sophisticated LP problems. Through an extensive examination of mathematical derivations and empirical research, the paper points out how these advancements successfully address the natural difficulties inherent in classical LP algorithms. The integration of these advances highlights the path of LP algorithm development, providing insights into their increased capabilities and use in contemporary optimization problems.