Slope stability analysis for high embankment roads is very important for infrastructure safety and its long life. This paper aims to review the stability of road embankments and its challenges. The factors associated with the stability of the road embankments are traffic loads, soil properties, and environmental conditions. Numerous researchers have studied the stability characteristics of road embankments using numerical, analytical, and experimental techniques. In the numerical method, both Finite Difference Method (FDM) and Finite Element Method (FEM) are often used for stability analysis of road embankments. Some of the common numerical based tools being used are PLAXIS, GeoStudio, ABAQUS, and FLAC, whereas analytical methods such as Bishop’s method and Morgenstern-price method are well established as well. Each and every analysis technique has its own merits and demerits in terms of material nonlinearity, failure phenomenon, complex geometry, and pore pressure. Some of the common challenges from the literature are poor drainage, inadequate pavement design, insufficient shoulder width, unrealistic assessment of magnitude and duration of vehicular loadings, embankment geometry, roadbed protection, width and slope angle, and enlargement of the surface area of the sliding mass. Additionally, the available and efficient strength improvement is reported from the historical case studies. This study highlights the interdisciplinary aspect of slope stability analysis by combining geotechnical engineering principles with advanced techniques like the Finite Element Method (FEM) and Finite Difference Method (FDM) to ensure the strength of road embankments subjected to different traffic and environmental conditions. In conclusion, this review identified the areas of additional research for real-time monitoring of slope instability for accurate prediction.