The modeling of turbulence, especially the high-speed compressible turbulence encountered in aerospace engineering, has always being a significant challenge in terms of balancing efficiency and accuracy. Most traditional models typically show limitations in universality, accuracy, and reliance on past experience. The stochastic multi-scale models show great potential in addressing these issues by representing turbulence across all characteristic scales in a reduced-dimensional space, maintaining sufficient accuracy while reducing computational cost. This review systematically summarizes advances in methods related to a widely used and refined stochastic multi-scale model, the One-Dimensional Turbulence (ODT). The advancements in formulations are emphasized for stand-alone incompressible ODT models, stand-alone compressible ODT models, and coupling methods. Some diagrams are also provided to facilitate more readers to understand the ODT methods. Subsequently, the significant developments and applications of stand-alone ODT models and coupling methods are introduced and critically evaluated. Despite the extensively recognized effectiveness of ODT models in low-speed turbulent flows, it is crucial to emphasize that there is still a research gap in the field of ODT coupling methods that are capable of accurately and efficiently simulating complex, three-dimensional, high-speed compressible turbulent flows up to now. Based on an analysis of the advantages and limitations of existing ODT methods, the recent advancement in the conservative compressible ODT model is considered to have provided a promising approach to tackle the modeling challenges of high-speed compressible turbulence. Therefore, this review outlines several recommended new research subjects and challenging issues to inspire further research in simulating complex, three-dimensional, high-speed compressible turbulent flows using ODT models.