Significant geotechnical challenges are happening in hilly areas with increasing urbanization and construction activities in hilly terrain. It is essential to ensure slope stability before and after construction to prevent catastrophic slope failures and casualties. Since the start of the twentieth century, many researchers have engaged in their research to calculate the safety factor for a two-dimensional slope for their simplicity and ease of calculation than a three-dimensional analysis. While traditional two-dimensional (2D) slope stability analysis methods are common, they often yield conservative estimates of the safety factor against failure and instability. In 1916, several dock collapses in Sweden prompted researchers to use the concept of slices and the equilibrium boundary approach to assess slope stability for the first time. The methodological approach developed by the Swedish Circle Method (Fellenius in Erdstatische Berechnungen mit Reibung und Kohäsion (Adhäsion) und unter Annahme kreiszylindrischer Gleitflächen. W. Ernst & Sohn, 1927). Later, researchers made several advancements to the Swedish method: Bishop’s Simplified Method of Slices (Géotech 5:7, 1955), Janbu’s Simplified Method (Embak-Dam Eng: Casagrande 5:47–86, 1956), Morgenstern and Price (Geotechnique 15(1):79–93, 1965), Spencer’s (Geotechnique 17:11–26, 1967), Sarma’s (Géotechnique 23:423, 1973), among others. This paper provides a brief history of the development of slope stability analysis and a comprehensive review of two-dimensional slope stability analysis, synthesizing the works of different researchers and highlighting critical methodologies, challenges, and the evolution of three-dimensional slope stability analysis. By elucidating the historical foundations and contemporary advancements, this review offers valuable insights for researchers, engineers, and practitioners engaged in slope stability assessment and mitigation strategies in hilly terrains.