Steel liquid storage tanks are critical elements of civil and industrial infrastructure, commonly used in water supply systems, petroleum storage, chemical processing, and firefighting facilities. Among the various structural challenges they face, buckling remains one of the most critical failure modes, particularly under seismic loads, wind forces, hydrostatic pressure and thermal gradients. This paper presents a comprehensive review of the buckling behaviour of steel liquid storage tanks, categorized across four major methodological domains: experimental investigations, analytical approaches, numerical simulations using Finite Element Analysis (FEA), and data-driven prediction models leveraging Artificial Neural Networks (ANN) and Machine Learning (ML). Experimental studies have been instrumental in uncovering the physical mechanisms of uplift, shell-wall interaction, and local instability, while analytical models have laid the groundwork for design standards. FEA has enabled advanced nonlinear simulations incorporating imperfection sensitivity, soil-structure interaction, and uplift behaviour. Recently, ANN models have demonstrated exceptional predictive accuracy in estimating buckling loads using geometric, material, and fabrication parameters, outperforming traditional code-based knockdown factors. Despite these advancements, significant research gaps remain, including the need for multi-physics modeling, inclusion of real-world degradation effects, and validation across elevated and non-standard tank configurations. The review emphasizes the growing potential of integrated frameworks combining experimental data, numerical simulations, and AI-driven tools. Future directions include the development of hybrid ANN–FEA platforms, real-time structural health monitoring systems, open-access data repositories, and digital twin technologies to support predictive diagnostics and lifecycle resilience. By bridging classical structural theory with modern computational intelligence, this review aims to guide the next generation of research and innovation in the safe, adaptive, and efficient design of liquid storage tank infrastructure.