This paper offers a comprehensive review of column-based ground improvement techniques, focusing on their fundamental mechanisms, design principles, construction methods, and field applications. It highlights stone columns and deep soil mixing (DSM) as the most widely used and effective solutions for enhancing the performance of weak and compressible soils. The core principles, including stress redistribution, increased shear strength, and accelerated consolidation, are discussed in detail. The review synthesizes key design parameters such as column geometry, area replacement ratio, and the role of geosynthetic reinforcement and load transfer platforms. It also examines the practical application of these methods through various case studies on embankments, tank foundations, and excavation supports. A dedicated section explores the pivotal role of numerical modeling, especially the finite element method (FEM), and emerging AI-driven approaches like Physics-Informed Neural Networks (PINNs) and surrogate modeling, which are shown to improve predictive accuracy and optimize the design process. Furthermore, the paper addresses critical challenges and limitations, including material variability, installation uncertainties, environmental impacts, and the need for enhanced quality control and long-term monitoring. It concludes by outlining future trends and innovations, such as the adoption of sustainable materials and the integration of machine learning for predictive design and real-time monitoring. This synthesis provides a structured overview of current best practices and offers valuable insights into the future direction of this vital area of geotechnical engineering.