The primary aim of every twenty-first century mining operation is to extract as much ore as possible in a safe and economical manner. Failure in mine excavation occurs when the shear stress acting on the rock is greater than the shear strength of the rock mass. The stability of rock slopes in open-pit mine and quarry operations is extremely important from both economic and safety points of view because unstable slopes can result in the loss of human life and damage to properties. This paper presents an overview of several case studies of slope failure in mining operations and explains various modes of failure in rock slopes, as well as factors that influence the stability of slope walls. With the aim of enforcing the importance of monitoring and evaluating slope stability in mining, both linear equilibrium and numerical modeling techniques were reviewed to elaborate their importance in designing stable slopes. In addition, the process of slope failure was discussed, and key signs of failure were indicated. In an effort to prevent mines from experiencing the hazards of slope failure, this study reports previous work performed in determining slope failure and the current state-of-the-art models, which entail the integration of analytical methods with artificial intelligence techniques. This innovation would help overcome the drawbacks of conventional prediction techniques that are cumbersome and ambiguous.